## Preprints

Coefficients of the inflated Eulerian polynomial, (with J.S. Auli, C.D. Savage).

Paperclip graphs, (with S. Butler, E.D. Demaine, M.L. Demaine, A. Hesterberg, J. Ku, J. Lynch, T. Tokieda).

Card guessing with partial feedback, (with P. Diaconis, X. He, S. Spiro), to appear in

*Combinatorics, Probability & Computing*.Guessing about guessing: Practical strategies for card guessing with feedback, (with P. Diaconis, S. Spiro).

## 2021

Permanental generating functions and sequential importance sampling, (with F. Chung, P. Diaconis),

*Advances in Applied Mathematics***126**(2021), 101916.On Levine's notorious hat puzzle, (with J. Buhler, C. Freiling, J. Kariv, J. Roche, M. Tiefenbruck, C. Van Alten, D. Yeroshkin),

*Integers***21A**(2021), #A8, 52pp.

## 2020

Slow Fibonacci walks, (with F. Chung and S. Spiro),

*Journal of Number Theory***210**(2020), 142-170.Some of my favorite problems, in

*50 Years of Combinatorics, Graph Theory, and Computing*, F. Chung, R. Graham, F. Hoffman, L. Hogben, R. Mullin, D. West, eds. CRC Press, 2020, 21-36.Efficient packings of unit squares in a large square, (with F. Chung),

*Discrete and Computational Geometry***64**(2020), 690-699.

## 2019

The magic of Charles Sanders Peirce, (with P. Diaconis), in

*The Mathematics of Various Entertaining Subjects, Volume 3*, J. Beineke, J. Rosenhouse, eds. Princeton University Press, 2019, 161-203.

## 2018

Maximally nontransitive dice, (with J. Buhler, A. Hales),

*American Mathematical Monthly***125**(2018), 387-399.Well dispersed sequences in [0,1]

^{d}, (with F. Chung),*Journal of Number Theory***189**(2018), 1-24.Sum sequences modulo

*n*, (with F. Chung and J. Folkman),*Journal of Combinatorial Theory, Series A***158**(2018), 290-314.The digraph drop polynomial, (with F. Chung), in

*Connections in Discrete Mathematics*, S. Butler, J. Cooper, G. Hurlbert, eds. Cambridge University Press, 2018, 86-103.Explicit error bounds for lattice Edgeworth expansions, (with J. Buhler, A. Gamst, A. Hales), in

*Connections in Discrete Mathematics*, S. Butler, J. Cooper, G. Hurlbert, eds. Cambridge University Press, 2018, 321-352.Permutations resilient to deletions, (with N. Alon, S. Butler and U. Rajkumar),

*Annals of Combinatorics***22**(2018), 673-680.Three-dimensional Floorplan Representations by Using Corner Links and Partial Order, (with I. Kang, F. Qiao, D. Kane, E.F.Y Young, and C.K. Cheng),

*ACM Transactions on Design Automation of Electronic Systems (TODAES)***24**(1), #13, 33 pp.Reflections on a theme of Ulam,

*Graph Theory, Favorite Conjectures and Open Problems*, R. Gera, T.W. Haynes, S.T. Hedetniemi, eds., Springer, 2018, 55-61.Tree structures and algorithms for physical designs, (with C.-K. Cheng, I. Kang, D. Park, X. Wang), ISPD '18L Proceedings of the 2018 International Symposium on Physical Design, March 2018, 120-125.

## 2017

Juggling card sequences, (with S. Butler, F. Chung and J. Cummings),

*Journal of Combinatorics***8**(2017), 507-539.The drop polynomial of a weighted digraph, (with F. Chung),

*Journal of Combinatorial Theory, Series B***126**(2017), 62-82. (errata)Parking distributions on trees, (with S. Butler and C. Yan),

*European Journal of Combinatorics***65**(2017), 168-185.Euclidean Ramsey Theory,

*Handbook of Discrete and Computational Geometry, 3rd ed.*, C.D. Toth, J. O'Rourke, J.E. Goodman, eds. CRC Press, 2017, #11, 16 pp.

## 2016

On the discrepancy of circular sequences of reals, (with F. Chung),

*Journal of Number Theory***164**(2016), 52-65.Inserting plus signs and adding, (with S. Butler and R. Stong),

*American Mathematical Monthly***123**(2016), 274-279.Anarchy is free in network creation, (with L. Hamilton, A. Levavi and P.-S. Loh),

*ACM Transactions on Algorithms***12**No. 2 (Feb 2016), Article 15, 10pp.The matrix cover polynomial, (with F. Chung),

*Journal of Combinatorics***7**(2016), 375-412.Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions, (with F. Chung and O. Braun),

*OR Spectrum***38**(2016), 531-540.The mathematics of the flip and horseshoe shuffles, (with S. Butler and P. Diaconis),

*American Mathematical Monthly***123**(2016), 542-556.3D Floorplan Representations: Corner Links and Partial Orders, (with F. Qiao, I. Kang, D. Kane, F.-Y. Young and C.-K. Cheng), in

*2016 IEEE International 3D Systems Integration Conference (3DIC 2016)*, IEEE (2016), 133-137.

## 2015

Ramsey theory & the probabilistic method. (with J. Spencer),

*Notices of the AMS***62**(2015), 132-136. (errata)Edge flipping in the complete graph, (with S. Butler, F. Chung and J. Cummings),

*Advances in Applied Mathematics***69**(2015), 46-64.Rudiments of Ramsey Theory, 2nd edition, (with S. Butler), AMS. (errata)

Egyptian fractions with each denominator having three distinct prime divisors, (with S. Butler and P. Erdos).

*INTEGERS: The Electronic Journal of Combinatorial Number Theory***15**(2015), A51, 9 pp.

(A solution of Egyptian fractions each with three distinct prime factors summing to one has been found by Emmanuel Vantieghem.)

## 2014

Unrolling residues to avoid progressions, (with S. Butler and L. Lu),

*Mathematics Magazine***87**(2014), 83-94.On the history of the Euclidean Steiner tree problem, (with M. Brazil, D.A. Thomas and M. Zachariasen),

*Archive for History of Exact Sciences***68**(2014), 327-354. (online link)de Bruijn sequences with varying combs, (with A. Alhakim and S. Butler),

*INTEGERS: The Electronic Journal of Combinatorial Number Theory***14A**(2014) #A1, 23 pp.Single-processor scheduling with time restrictions, (with O. Braun and F. Chung),

*Journal of Scheduling***17**(2014), 399-403. (online link)Unseparated pairs and fixed points in random permutations, (with P. Diaconis and S. N. Evans),

*Advances in Applied Mathematics***61**(2014), 102-124.

## 2013

Inversion-descent polynomials for restricted permutations, (with F. Chung),

*Journal of Combinatorial Theory, Series A***120**(2013), 366-378. (erratum)Remembering Erdos,

*Math Horizons*April 2013, 11-12.Paul Erdos and Egyptian Fractions, in

*Erdos Centennial*, L. Lovasz, I. Ruzsa, V. T. Sos and D. Palvolgyi eds., Bolyai Society Mathematical Studies 25, Springer-Verlag, Heidelberg (2013), 289-309.Ramsey theory in the work of Paul Erdos, (with J. Nesetril), in

*The Mathematics of Paul Erdos*, R. Graham, J. Nesetril and S. Butler eds., Springer-Verlag, New York, 2013, 171-193.Juggling mathematics and magic,

*Notices of the International Congress of Chinese Mathematicians***1**(2013), 7-9.Subdivision using angle bisectors is dense in the space of triangles, (with S. Butler),

*The American Mathematical Monthly***120**(2013), 622-630.A note on irregularities of distributions,

*INTEGERS: Electronic Journal of Combinatorial Number Theory***13**(2013), #A53, 4 pp.Constructing points through folding and intersection, (with S. Butler, E. Demaine and T. Tachi),

*International Journal of Computational Geometry & Applications***23**(2013), 49-64.An interstice relationship for flowers with four petals, (with S. Butler, G. Guettler and C. Mallows),

*Journal of Geometry***104**(2013), 421-438. (online link)Anarchy is free in network creation. (with L. Hamilton, A. Levavi and P.-S. Loh),

*Proceedings of WAW 2013*, LNCS 8305 (2013), 220-231.

## 2012

Edge flipping in graphs, (with F. Chung),

*Advances in Applied Mathematics***48**(2012), 37-63.A note on marking lines in [

*k*]^{n}, (with S. Butler),*Designs, Codes and Cryptography***65**(2012), 165-175.Generalized Eulerian sums, (with F. Chung),

*Journal of Combinatorics***3**(2012), 299-316.Origami rings, (with J. Buhler, S. Butler and W. de Launey),

*Journal of the Australian Mathematical Society***92**(2012), 299-311.

## 2011

Bus matrix synthesis based on Steiner graphs for power efficient system-on-chip communications, (with R. Wang, Y. Zheng, N.-C. Chou, E.F.Y. Young and C.-K. Cheng),

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems***30**(February 2011), 167-179.Memories of Martin Gardner, (with S.G. Krantz, P.W. Diaconis, D.E. Knuth, J. Randi, P. Renz and R.M. Smullyan),

*Notices Amer. Math. Soc.***58**(2011), 418-422.Hypercube orientations with only two in-degrees, (with J. Buhler, S. Butler and E. Tressler),

*Journal of Combinatorial Theory, Series A***118**(2011), 1695-1702.Is randomness necessary?,

*Randomness Through Computation: Some Answers, More Questions*, H. Zenil, ed., World Scientific Press (2011), 3-5.Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks, (with P. Diaconis), Princeton University Press, 244 pp., 2011. (Errata)

## 2010

Some Ramsey results for the

*n*-cube, (with J. Solymosi),*Journal of Combinatorial Theory, Series A***117**(2010), 189-195.A panoramic view (review of

*The Princeton Companion of Mathematics*),*American Scientist***98**(January/February 2010), 78-79.Enumerating (multiplex) juggling sequences, (with S. Butler),

*Annals of Combinatorics***13**(2010), 413-424.How to play the majority game with a liar, (with S. Butler and J. Mao),

*Discrete Mathematics***310**(6 February 2010), 622-629.A symmetrical Eulerian identity, (with F. Chung and D. Knuth),

*Journal of Combinatorics***1**(2010), 29-38.Descent polynomials for permutations with bounded drop size, (with F. Chung, A. Claesson and M. Dukes),

*European Journal of Combinatorics***31**(2010), 1853-1867. (errata)Irreducible Apollonian configurations and packings, (with S. Butler, G. Guettler and C. Mallows),

*Discrete & Computational Geometry***44**(2010), 487-507.Shuffling with ordered cards, (with S. Butler),

*Journal of Combinatorics***1**(2010), 121-139.Can you hear the shape of a Beatty sequence, (with K. O'Bryant),

*Additive Number Theory: Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson*, D. Chudnovsky, G. Chudnovsky, eds. (2010), 39-52.Tiling polygons with lattice triangles, (with S. Butler, F. Chung and M. Laczkovich),

*Discrete & Computational Geometry***44**(2010), 896-903.Physical synthesis of bus matrix for high bandwidth low power on-chip communications, (with R. Wang, E.F.Y. Young and C.-K. Cheng),

*Proceedings of the 19th international symposium on Physical design*(2010), 91-96.Iterated triangle partitions, (with S. Butler),

*Fete of Combinatorics and Computer Science*, G. Katona, A. Schrijver, T. Szonyi, eds., Bolyai Society Mathematical Studies 20, Springer-Verlag, Heidelberg (2010), 23-42.Finding patterns avoiding many monochromatic constellations, (with S. Butler and K. Costello),

*Experimental Mathematics***19**(2010), number 4, 399-411.Open problems in Euclidean Ramsey theory, (with E. Tressler), in

*Ramsey Theory: Yesterday, Today and Tomorrow*, A. Soifer (ed), Birkhauser, Boston (2010), 115-120

## 2009

Approximately optimal trees for group key management with batch updates, (with M. Li, Z. Feng, N. Zang and F.F. Yao),

*Theoretical Computer Science***410**(2009), 1013-1021.Minimum perimeter rectangles that enclose congruent non-overlapping circles, (with B.D. Lubachevsky),

*Discrete Mathematics***309**(2009), 1947-1962.Packing equal squares into a large square, (with F. Chung),

*JCTA***116**(2009), 1167-1175.Optimal jumping patterns, (with S. Butler and N. Zang),

*Journal of Combinatorics and Number Theory***1**(2009), 1-13.The elementary proof of the prime number theorem, (with J. Spencer),

*The Mathematical Intelligen**c**er***31**(2009), 18-23.

## 2008

Quasi-random graphs with given degree sequences, (with F.R.K. Chung),

*Random Structures and Algorithms***32**(2008), 1-19.Enumerating split-pair arrangements, (with N. Zang),

*JCTA***115**(2008), 293-303.Primitive juggling sequences, (with F.R.K. Chung),

*American Mathematical Monthly***115**(March 2008), 185-194.Analysis of greedy approximations with nonsubmodular potential functions, (with D.-Z. Du, P.M. Pardalos, P.-J. Wan, W. Wu and W. Zhao),

*Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms*(2008), 167-175.Products of universal cycles, (with P. Diaconis),

*A Lifetime of Puzzles: Honoring Martin Gardner*, E. Demaine, M. Demaine, T. Rodgers, eds. (2008), 35-55.Old and new problems and results in Ramsey theory,

*Horizons of Combinatorics (Bolyai Society Mathematical Studies)*, E. Gyori, G.O.H. Katona and L. Lovasz, eds. (2008), 105-118.Jumping sequences, (with S. Butler and N. Zang),

*Journal of Integer Sequences***11**(2008), article 08.4.5, 13pp.3-D floorplanning using labeled tree and dual sequences, (with C.-K. Cheng, F.R.K. Chung, R. Wang, E.F.Y. Young, Y. Zhu), in

*Proceedings of the 2008 international symposium on physical design*, ACM, New York, NY, 54-59.

## 2007

The solutions to Elmsley's problem, (with P. Diaconis),

*Math Horizons***14**(2007), 22-27. (errata, errata)On minimal colorings without monochromatic solutions to a linear equation, (with B. Alexeev and J. Fox),

*Combinatorial Number Theory*, B. Landman, M.B. Nathanson, J. Nesetril, R.J. Nowakowski, C. Pomerance, eds. (2007), 1-22. Also appeared in*INTEGERS***7**(2) (2007), A1 (electronic) 20 pp.Universal juggling cycles, (with F.R.K. Chung),

*Combinatorial Number Theory*, B. Landman, M.B. Nathanson, J. Nesetril, R.J. Nowakowski, C. Pomerance, eds. (2007), 121-130. Also appeared in*INTEGERS***7**(2) (2007), A8 (electronic) 10 pp.Some of my favorite problems in Ramsey Theory,

*Combinatorial Number Theory*, B. Landman, M.B. Nathanson, J. Nesetril, R.J. Nowakowski, C. Pomerance, eds. (2007), 229-236. Also appeared in*INTEGERS***7**(2) (2007), A15 (electronic) 8 pp.Approximately optimal trees for group key management with batch updates, (with Z. Feng, M. Li, F.F. Yao),

*Theory and Applications of Models of Computation*, Lecture Notes in Computer Science**4484**, Springer-Verlag, Heidelberg, J.-Y. Cai, S.B. Cooper and H. Zhu, eds. (2007), 284-295.How to play the majority game with liars, (with S. Butler and J. Mao),

*AAIM 2007*, Lecture Notes in Computer Science**4508**, Springer-Verlag, Heidelberg, M.-Y. Kao and X.-Y. Li, eds. (2007), 221-230.Optimal tree structure for group key management with batch updates, (with M. Li and F.F. Yao),

*SIAM J. on Disc. Math***21**(2007), no. 2, 532-547.Reducing the bias of multitaper spectrum estimates, (with G.A. Prieto, R.L. Parker, D.J. Thomson, and F.L. Vernon),

*Geophysical Journal International***171**(2007), 1269-1281.Oblivious and adaptive strategies for the Majority and Plurality problems, (with F.R.K. Chung, J. Mao, and A. Yao),

*Algorithmica***48**(2007), 147-157.

## 2006

Apollonian circle packings: geometry and group theory II. Super-Apollonian group and integral packings, (with J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C.H. Yan),

*Discrete & Computational Geometry***35**(2006), no. 1, 1-36.Apollonian circle packings: geometry and group theory III. Higher dimensions, (with J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C.H. Yan),

*Discrete & Computational Geometry***34**(2006), no. 1, 37-72.Monochromatic equilateral right triangles on the integer grid, (with J. Solymosi),

*Topics in Discrete Mathematics*, Algorithms and Combinatorics**26**, 129-132.On the growth of a van der Waerden-like function,

*INTEGERS***6**(2006), A29 (electronic) 5 pp.Review of "Modern Graph Theory" by Reinhard Diestel, (with P. Diaconis),

*SIAM Review***48**, no. 4, (2006), 798-800.Maximizing Data Locality in Distributed Systems, (with F.R.K. Chung, R. Bhagwan, S. Savage, and G.M. Voelker),

*Jour. Comp. System Sci.***72**(December 2006), 1309-1316.Communication Latency Aware Low Power NoC Synthesis, (with Y. Hu, Y. Zhu, H. Chen and C.-K. Cheng), appeared in proceedings of

*Design Automation Conference, 2006 43rd ACM/IEEE*, 574-579.Parallelism versus memory allocation in pipelined router forwarding engines, (with F.R.K. Chung, J. Mao and G. Varghese),

*Theory of Computing Systems***39**(November 2006), 829-849.Timing model reduction for hierarchical timing analysis, (with S. Zhou, Y. Zhu, Y. Hu, M. Hutton, and C.-K. Cheng),

*Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design*, 415-422.On the construction of zero-deficiency parallel prefix circuits with minimum depth, (with H. Zhu, and C.-K. Cheng),

*ACM Transactions on Design Automation of Electronic Systems***11**No. 2 (April 2006), 387-409.

## 2005

Constructing zero-deficiency parallel prefix adder of minimum depth, (with H. Zhu, and C.-K. Cheng),

*Proceedings of the 2005 conference on Asia South Pacific design automation*, 883-888.A discrete Fourier kernel and Fraenkel's tiling conjecture, (with K. O'Bryant),

*Acta Arithmetica***118**(2005), no.3, 283-304.Apollonian circle packings: geometry and group theory I. The Apollonian group, (with J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C.H. Yan),

*Discrete & Computational Geometry***34**(2005), no. 4, 547-585.Oblivious and Adaptive Strategies for the Majority and Plurality Problems, (with F.R.K. Chung, J. Mao, and A. Yao),

*Computing and combinatorics*, Lecture Notes in Computer Science**3595**, Springer, Berlin (2005), 329-338.

## 2004

Generalized de Bruijn cycles, (with J.N. Cooper),

*Ann. Comb.***8**(2004), no. 1, 13-25.Guessing secrets with inner product questions, (with F.R.K. Chung and L. Lu),

*Internet Math.***1**(2004), no. 2, 177-192.Parallelism versus Memory Allocation in Pipelined Router Forwarding Engines, (with F.R.K. Chung and G. Varghese), SPAA'04, Barcelona, Spain, (2004), 103-111.

Open problems in Euclidean Ramsey Theory,

*Geombinatorics***13**(2004), 165-177.Juggling patterns, passing, and posets, (with J. Buhler),

*Mathematical Adventures for Students and Amateurs*, MAA (2004), 99-116.

## 2003

Dense packings of congruent circles in rectangles with a variable aspect ratio, (with B.D. Lubachevsky), in

*Discrete and computational geometry*, 633-650, Algorithms Combin., 25, Springer, Berlin, 2003.Apollonian circle packings: number theory, (with J.C. Lagarias, C.L. Mallows, A.R. Wilks, and C.H. Yan),

*J. Number Theory***100**(2003), no. 1, 1-45.Floorplan Representations: Complexity and Connections, (with B. Yao, H. Chen, and C.-K. Cheng), ACM Trans. on Design Automation of Electronic Systems, vol. 8, pp. 55-80, Jan. 2003.

A Hierarchical Three-Way Interconnect Architecture for Hexagonal Processors, (with F. Zhou, E.Y. Cheng, B. Yao, and C.-K. Cheng), Int. Workshop on System Level Interconnect Prediction, pp. 133-139, April 2003.

Finding favorites, (with F.R.K. Chung, J. Mao, and A. Yao), Electronic Colloquium on Computational Complexity, Report No. 78 (2003).

## 2002

Ramsey properties of families of graphs, (with T. Luczak, V. Rodl, and A. Rucinski),

*J. Combin. Theory Ser. B***86**(2002), no. 2, 413-419.New bounds on a hypercube coloring problem, (with H.Q. Ngo and D.-Z. Du),

*Inform. Process. Lett.***84**(2002), no. 5, 265-269.Sparse quasi-random graphs, (with F.R.K. Chung), Special issue: Paul Erdos and his mathematics,

*Combinatorica***22**(2002), no. 2, 217-244.On sparse sets hitting linear forms, (with F.R.K. Chung and P. Erdos),

*Number theory for the millennium, I (Urbana, IL, 2000)*, 257-272, A K Peters, Natick, MA, 2002.Ramsey theory and Paul Erdos (recent results from a historical perspective), (with J. Nevsetvril),

*Paul Erdos and his mathematics, II (Budapest, 1999)*, 339-365, Bolyai Soc. Math. Stud., 11, Janos Bolyai Math. Soc., Budapest, 2002.Balancing the Interconnect Topology for Arrays of Processors between Cost and Power, (with E.Y. Cheng, F. Zhou, B. Yao, and C.-K. Cheng), IEEE Int. Conf on Computer Design, pp. 30-35, Sept. 2002.

Guessing secrets with inner product questions, (with F.R.K. Chung and L. Lu),

*Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms*, 247-253, 2002.

## 2001

Combinatorics for the East model, (with F.R.K. Chung and P. Diaconis),

*Adv. in Appl. Math.***27**(2001), no. 1, 192-206.Guessing secrets (extended abstract), (with F.R.K. Chung and T. Leighton),

*Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (Washington, DC, 2001)*, 723-726, SIAM, Philadelphia, PA, 2001.Distance realization problems with applications to internet tomography, (with F.R.K. Chung, M. Garrett and D. Shallcross),

*J. Comput. System Sci.***63**(2001), no. 3, 432-448.Dynamic location problems with limited look-ahead, (with F.R.K. Chung), Computing and combinatorics (Taipei, 1998).

*Theoret. Comput. Sci.***261**(2001), no. 2, 213-226.On bipartite graphs with linear Ramsey numbers, (with V. Rodl and A. Rucinski), Paul Erdos and his mathematics (Budapest, 1999).

*Combinatorica***21**(2001), no. 2, 199-209.Guessing secrets, (with F.R.K. Chung and T. Leighton),

*Electron. J. Combin.***8**(2001), no. 1, Research Paper 13, 25 pp. (electronic).Statistical problems involving permutations with restricted positions, (with P. Diaconis and S.P. Holmes),

*State of the art in probability and statistics (Leiden, 1999)*, 195-222, IMS Lecture Notes Monogr. Ser., 36, Inst. Math. Statist., Beachwood, OH, 2001.Revisiting Floorplan Representations, (with B. Yao, H. Chen, and C.K. Cheng), Int. Symp. on Physical Design, 2001, pp. 138-143.

New bounds on a hypercube coloring problem and linear codes, (with H.Q. Ngo, and D.Z. Du),

*Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC '01)*.

## 2000

Improving dense packings of equal disks in a square, (with D.W. Boll, J. Donovan and B.D. Lubachevsky),

*Electron. J. Combin.***7**(2000), Research Paper 46, 9 pp. (electronic).On graphs with linear Ramsey numbers, (with V. Rodl and A. Rucinski),

*J. Graph Theory***35**(2000), no. 3, 176-192.

## 1999

The Graph of Generating Sets of an Abelian Group, (with Persi Diaconis),

*Colloq. Math.***80**(1999), 31-38.On the Set of Common Differences in van der Waerden's Theorem on Arithmetic Progressions, (with T.C. Brown and B.M. Landman)

*Canad. Math. Bull.***42**(1999), 25-36.On the Limit of a Recurrence Relation, (with C. Yan),

*J. of Difference Equations Appl.***5**(1999), 71-95.**Erdos on Graphs: His Legacy of Open Problems**, (with F.R.K. Chung), A.K. Peters, Cambridge, MA 1993, xiv+142 pp.

## 1998

Dense Packings of Congruent Circles in a Circle, (with B.D. Lubachevsky, K.J. Nurmela, P.R.J. Ostergard),

*Discrete Math.***181**(1998), 139-154.Forced Convex

*n*-gons in the Plane, (with F.R.K. Chung),*Discrete and Computational Geometry***19**, (1998), 367-371.The Work of Peter Shor,

*Proceedings of the International Congress of Mathematicians, Vol. I (Berlin)*, Doc. Math. 1998, Extra Vol. I, 133-140.

## 1997

The Steiner Ratio for the dual normed plane, (with D.Z. Du and P.J. Wan),

*Discrete Mathematics***171**(1997), 261-275.Curved Hexagonal Packings of Equal Disks in a Circle, (with B.D. Lubachevsky),

*Discrete and Computational Geometry***18**(1997), 179-194.Patterns and Structures in Disk Packings, (with B.D. Lubachevsky and F.H. Stillinger),

*Periodica Mathematica Hungarica***34**(1-2), (1997), 123-142.Euclidean Ramsey Theory,

*Handbook of Discrete and Computational Geometry*, E. Goodman and J. O'Rourke, editors, (1997), 153-166.Random walks on generating sets for finite groups, (with F.R.K. Chung),

*Electronic J. Combin.***4**(1997), no. 2, Research Paper 7, approx. 14pp. (electronic)Stratified Random Walks on the

*n*-Cube (alternate), (with F.R.K. Chung),*Random Structures and Algorithms***11**(1997), 199-222.

## 1996

Ramsey Theory in the Work of Paul Erdos, (with J. Nesetril), in

*The Mathematics of Paul Erdos, Volume 2*, Springer, Berlin, 1996, 193-209.Primitive Partition Identities, (with P. Diaconis and B. Sturmfels),

*Paul Erdos is 80, Vol. 2*, Janos Bolyai Society, Budapest, Hungary (1996) 173-192.A Remark on a Paper of Erdos and Nathanson,

*Number Theory, New York Seminar 1991-1995*, D.V. Chudnowsky, G.U. Chudnovsky, M. Nathanson, eds. Springer-Verlag, New York 1996, 177-179.On Schur properties of random subsets of integers, (with V. Rodl and A. Rucinski),

*J. Number Theory***61**(1996), 388-408.Complete sequences of sets of integer powers, (with S.A. Burr, P. Erdos and W. Li),

*Acta Arithmetica***77**(1996), 133-138.On sampling with Markov chains, (with F.R.K. Chung and S.T. Yau),

*Random Structures and Algorithms***9**(1996), 55-77.Repeated Patterns of Dense Packings of Equal Disks in a Square, (with B.D. Lubachevsky),

*Elec. J. of Combinatorics***3**(1996) R16, 17 pp.

## 1995

Dense Packings of Equal Disks in an Equilateral Triangle: From 22 to 34 and Beyond, (with B.D. Lubachevsky),

*Electronic J. Combinatorics*#A1, 1995 (January), 39 pp.Dense Packings of 3

*k*(*k*+1)+1 Equal Disks in a Circle for*k*=1,2,3,4, and 5, (with B.D. Lubachevsky),*Computing and Combinatorics, Fifth Annual International Conference, COCOON '95 Xi'an China, August 1995 Proceedings*, (1995), 303-312, Springer-Verlag, NY.Pebbling a Chessboard, (with F.R.K. Chung, J. Morrison and A.M. Odlyzko),

*American Math. Monthly***102**(1995), 113-123.On the Cover Polynomial of a Digraph, (with F.R.K. Chung),

*Journal of Combinatorial Theory, (B)***65**(1995), 273-290.A Tight Lower Bound for the Steiner Ratio in Minkowski Planes, (with B. Gao and D.Z. Du),

*Discrete Mathematics***142**(1995), 49-63.

## 1994

Juggling Drops and Descents, (with J. Buhler, D. Eisenbud and C. Wright),

*American Math Monthly***101**(1994) 507-519. Reprinted with new appendix in the*Canadian Mathematical Society, Conference Proceedings, Volume 20, 1997*.A Note on the Binomial Drop Polynomial of a Poset, (with J. Buhler),

*J. Comb. Th. (A)***66**(1994) 321-326.The tight lower bound for the Steiner ratio in Minkowski planes, (with B. Gao, D.Z. Du),

*Proceedings of the 10th Symp. on Computational Geometry, Stony Brook, NY, ACM, (1994)*183-191.Routing permutations on graphs via matchings, (with N. Alon, F.R.K. Chung),

*SIAM Journal on Discrete Mathematics***7**(1994), 513-530.Recent Trends in Euclidean Ramsey Theory,

*Discrete Math.***136**(1994), 119-127.

## 1993

Lexicographic Ramsey Theory, (with P.C. Fishburn),

*J. Combin. Th. (A)***62**(1993) 280-298.On hypergraphs having evenly distributed subhypergraphs, (with F.R.K. Chung),

*Disc. Math.***111**(1993) 125-129.Graceful Configurations in the Plane, (with D. Chung and H. Taylor),

*Mathematics Magazine***66**no. 2, (1993) 96-104.The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle, (with A.R. Calderbank, P. Frankl, W-C W. Li, L.A. Shepp),

*Journal of Algebraic Combinatorics***3**(1993) 31-48.Minimum Steiner Trees in Normed Planes, (with D.Z. Du, B. Gao, Z.-C. Liu, and P.-J. Wan),

*Disc. & Comp. Geo.***9**(1993) 351-370.**An Introduction to Discrete Mathematics**, (with J. Akiyama), (1993) (in Japanese), Asakura Publishing Co.Routing permutations in graphs via matchings, (with N. Alon and F.R.K. Chung),

*Proceedings of the 25th ACM Symposium on Theory of Computing*, pp. 583-591, San Diego, CA.

## 1992

An Affine Walk on the Hypercube, (with P. Diaconis),

*Journal of Computational and Applied Mathematics***41**(1992), 215-235.Bounds for Arrays of Dots with Distinct Slopes or Lengths, (with P. Erdos, I.Z. Ruzsa, H. Taylor),

*Combinatorica***12**(1) (1992) 39-44.Quasi-random subsets of

*Z*_n, (with F.R.K. Chung),*J. Comb. Th (A)***61**(1992) 64-86.Binomial coefficient codes over GF(2), (with P. Diaconis),

*Discrete Math.***106/107**(1992) 181-188.Maximum cuts and quasi-random graphs, (with F.R.K. Chung),

*Proceedings of Poznan 1989 Symposium on Random Graphs***2**, 23-33 (1992) A.M. Frieze and T. Luczak, eds., John Wiley publishers.Universal cycles for combinatorial structures, (with F.R.K. Chung and P. Diaconis),

*Discrete Math.***110**(1992) 43-59.Cohomological Aspects of Hypergraphs, (with F.R.K. Chung),

*Trans. of the Amer. Math. Soc.***334**no. 1 (1992) 365-388.Roots of Ramsey Theory,

*Andrew M. Gleason, Glimpses of a Life in Mathematics*39-47, E. Bolker, P. Cherno, C. Costes, D. Lieberman, eds. (1992), E. Bolker, pub.

## 1991

Quasi-random Set Systems, (with F.R.K. Chung),

*J. Amer. Math. Soc.***4**(1991), 151-196.Further Results on Maximal Anti-Ramsey Graphs, (with S.A. Burr, P. Erdos, and P. Frankl),

*Proceedings of 6th Quadrennial International Conference on Theory and Applications of Graphs, Western Michigan University*, in Graph Theory, Combinatorics, and Applications, Y. Alavi, G. Chartrand, O.R. Oellerman, A.J. Schwenk, eds. (1991), 193-206.Quasi-Random Tournaments, (with F.R.K. Chung),

*Journal of Graph Theory***15**no. 2 (1991) 173-198.

## 1990

Penny-Packing and Two-Dimensional Codes, (with N.J.A. Sloane),

*Discrete and Computational Geometry***5**(1990), 1-11.Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions, (with P. Diaconis and J.A. Morrison),

*Random Structures and Algorithms*(1990), 51-72.Iterated Combinatorial Density Theorems, (with P. Frankl and V. Rodl),

*Journal of Combinatorial Theory, Series A***54**(1990), 95-111.Quasi-Random Hypergraphs, (with F.R.K. Chung),

*Random Structures and Algorithms***1**(1990), 105-124.Ramsey Theory, (with Joel H. Spencer),

*Scientific American***262**no. 7 (1990), 112-117.Quantitative Versionen von kombinatorischen Partitionssatzen, (with P. Frankl, and V. Rodl)

*Jber. d. Dt. Math.-Verein***92**(1990), 130-144.A Whirlwind Tour of Computational Geometry, (with F. Yao),

*American Mathematical Monthly***97**(1990), 687-701.Balanced Design of Bootstrap Simulations, (with D.V. Hinkley, P.W.M. John, and S. Shi),

*J. of Royal Stat. Soc. (B)***52**(1990), 185-202.On Graphs Not Containing Prescribed Induced Subgraphs, (with F.R.K. Chung),

*A Tribute to Paul Erdos*, ed. by A. Baker, B. Bollobas and A. Hajnal, Cambridge University Press (1990), 111-120.**Ramsey Theory**, (with B. Rothschild and J.H. Spencer), John Wiley and Sons, NY, 2nd edition, xii+196pp.Topics in Euclidean Ramsey Theory,

*Mathematics of Ramsey Theory*, J. Nesetril and V. Rodl, eds. Springer-Verlag, New York, (1990), 200-213.Quantitative Forms for Combinatorial Partition and Density Theorems, (with P. Erdos, P. Frankl, and V. Rodl),

*Proceedings of Bernoulli Soc. Meeting of Tashkent, Uzbekistan (1990)*.

## 1989

The Shortest-Network Problem, (with M.W. Bern),

*Scientific American***260**(1989) 84-89.Steiner Trees on a Checkerboard, (with F.R.K. Chung and M. Gardner),

*Math. Mag.***62**(1989) 83-96.A Dynamic Location Problem for Graphs, (with F.R.K. Chung and M.E. Saks),

*Combinatorica***9**(1989), 111-131.Maximal Antiramsey Graphs and the Strong Chromatic Number, (with S.A. Burr, P. Erdos, V.T. Sos),

*Journal of Graph Theory***13**(1989) 263-282.Quasi-Random Graphs, (with F.R.K. Chung and R.M. Wilson),

*Combinatorica***9**(1989), 345-362.Quasi-random hypergraphs, (with F.R.K. Chung),

*Proc. Natl. Acad. Sci.***86**(1989), 8175-8177.**Concrete Mathematics**, (with D.E. Knuth and O. Patashnik), Addison Wesley, (1989) 7th Printing, July 1991, 625 pp. + xiii. (Chinese edition, Taipei, 1990, 731 pp.)On the Improbability of Reaching Byzantine Agreements, (with A.C. Yao),

*Proc. 21st ACM Symp. on Th. of Comp. (1989)*, 467-478.On the Distribution of Monochromatic Configurations, (with P. Frankl and V. Rodl),

*Irregularities of Partitions*, Springer-Verlag, Algorithms and Combinatorics**8**(1989), 71-87.Old and New Proofs of the Erdos-Ko-Rado Theorem, (with P. Frankl),

*Journal of Sichuan University Natural Science Edition***26**(1989), Special Issue.

## 1988

On the Fractional Covering Number of Hypergraphs, (with F.R.K. Chung, Z. Furedi, and M.R. Garey),

*SIAM J. Disc. Math.***1**(1988) 45-49.Pursuit-Evasion Games on Graphs, (with F.R.K. Chung and J.E. Cohen),

*J. of Graph Theory***12**(1988) 159-167.Isometric Embedding of Graphs,

*Selected Topics in Graph Theory 3*, Beineke/Wilson eds., Academic Press, N.Y., (1988), 133-150.QuasiRandom Graphs, (with F.R.K. Chung and R.M. Wilson),

*Proc. Natl. Acad. Sci.***85**(1988) 969-970.Quantitative Theorems for Regular Systems of Equations, (with P. Frankl and V. Rodl),

*J. of Comb. Th. (A)***47**(1988) 246-261.On Induced Subgraphs of the Cube, (with F.R.K. Chung, Z. Furedi, and P. Seymour),

*J. Combin. Th. (A)*(1988), 180-187.

## 1987

Induced Restricted Ramsey Theorems for Spaces, (with P. Frankl and V. Rodl),

*Jour. Comb. Th. (A)***44**(1987), 120-128.On Subsets of Abelian Groups with No 3-Term Arithmetic Progression, (with P. Frankl and V. Rodl),

*Jour. Comb. Th. (A)***45**(1987), 157-161.Highly Irregular Graphs, (with Y. Alavi, G. Chartrand, F.R.K. Chung, P. Erdos and O.R. Oellermann),

*J. of Graph Theory***11**(1987) 235-249.Numbers in Ramsey Theory, (with V. Rodl),

*Surveys in Combinatorics*, London Math. Soc. Lect. Notes Series 123, ed. C. Whitehead (1987) 111-153.Random Walks Arising in Random Number Generation, (with F.R.K. Chung and P. Diaconis),

*Annals of Probability***15**(1987) 1148-1165.Dynamic Search in Graphs, (with F.R.K. Chung and M.E. Saks),

*Perspectives in Computing, Vol. 15, Discrete Algorithms and Complexity, Proc. Japan-US Joint Seminar 6/86, Kyoto, Japan, (1987)*351-387.A New Result on Comma-Free Codes of Even Word-Length, (with B. Tang and S.W. Golomb),

*Can. J. Math.***39**(1987) 513-526.A Similarity Measure for Graphs - Reflections on a Theme of Ulam,

*Los Alamos Science*No. 15 (special issue) (1987), 114-121.The Radon Transform on Abelian Groups, (with P. Frankl),

*Jour. of Combinatorial Theory (A)***44**(1987) 168-171.

## 1986

Mathematics is a Very Exciting Subject, (in Japanese with J. Akiyama),

*Sugaku Seminar***25**(1986), 21-32.Large Minimal Sets Which Force Long Arithmetic Progressions, (with J. Nesetril),

*Jour. Comb. Th. (A)***42**(1986), 270-276.Some Intersection Theorems for Ordered Sets and Graphs, (with F.R.K. Chung, P. Frankl and J.B. Shearer),

*Jour. Comb. Th. (A)***43**(1986), 23-37.

## 1985

On the Covering Radius of Codes, (with N.J.A. Sloane),

*IEEE Trans. Inf. Theory*IT-31 (1985), 385-401.Old and New Euclidean Ramsey Theorems,

*Dis. Geo. and Convexity, Annals of the N.Y. Acad. Sci.***440**(1985), 20-30.On the Addressing Problem for Directed Graphs, (with F.R.K. Chung and P.M. Winkler),

*Graphs and Comb.***1**(1985), 41-50.The Radon Transform on

*Z*_2^*k*, (with P. Diaconis),*Pacific Jour. Math.***118**(1985), 323-345.Quantitative Forms of a Theorem of Hilbert, (with T.C. Brown, P. Erdos, and F.R.K. Chung),

*Jour. Comb. Theory (A)***38**(1985), 210-216.On Isometric Embeddings of Graphs, (with P.M. Winkler),

*Trans. Amer. Math. Soc.***288**(1985), 527-536.On the History of the Minimum Spanning Tree Problem, (with P. Hell),

*Annals Hist. of Comp.***7**(1985), 43-57.Intersection Theorems for Vector Spaces, (with P. Frankl),

*Europ. Jour. Comb.***6**(1985) 183-187.A New Bound for Euclidean Steiner Minimal Trees, (with F.R.K. Chung),

*Dis. Geo. and Convexity, Annals N.Y. Acad. Sci.***440**(1985) 328-346.Classes of Interval Graphs under Expanding Length Restrictions, (with P.C. Fishburn),

*Jour. Graph Th.***9**(1985) 459-472.

## 1984

Isometric Embeddings of Graphs, (with P.M. Winkler),

*Proc. Natl. Acad. Sci.***81**(1984), 7259-7260.On Isometric Embeddings of Graphs,

*Progress in Graph Th.*eds. J.A. Bondy and U.S.R. Murty, Academic Press, Canada (1984), 307-322.Anti-Hadamard Matrices, (with N.J.A. Sloane),

*Lin. Algebra and its Applic.***62**(1984), 113-137.Fountains, Showers, and Cascades - Juggling's quintessential combinations of algebra and acrobatics, (with Joe Buhler),

*The Sciences*(1984), 44-51. (Also as "Juggling,"*MD Magazine***29**(1985), 153-166.)Combinatorial Designs Related to the Perfect Graph Conjecture, (with V. Chvatal, A.F. Perold and S.H. Whitesides),

*Annals of Disc. Math.***21**(1984), 197-206.

## 1983

Recent Developments in Ramsey Theory,

*Proc. Int'l. Congress of Math., Warszawa*, Polish Scientific Publishers and Elsevier Science Publishing Co., (1983), 1555-1567.Edge-Colored Complete Graphs with Precisely Colored Subgraphs, (with F.R.K. Chung),

*Combinatorica***3**(1983), 315-324.A Canonical Partition Theorem for Equivalence Relations on

*Z*^*t*, (with W. Deuber, H.J. Promel, and B. Voigt),*Jour. Comb. Theory (A)***34**(1983), 331-339.Euclidean Ramsey Theorems on the

*n*-Sphere,*Jour. Graph Theory***7**(1983), 105-114.The Mathematics of Perfect Shuffles, (with P. Diaconis and W.M. Kantor),

*Adv. Applied Math.***4**(1983), 175-196.On Universal Graphs for Spanning Trees, (with F.R.K. Chung),

*Jour. London Math. Soc.***27**(1983) 203-211.On Complete Bipartite Subgraphs Contained in Spanning Tree Complements, (with B. Bollobas and F.R.K. Chung),

*Studies in Pure Math.*, Akad. Kiado, Birkhauser, (1983), 83-90.Combinatorial Scheduling Th. Part II,

*Chinese Journal of Operations Research***2**(1983), 26-35.Finding the Convex Hull of a Simple Polygon, (with F. Yao),

*J. Algorithms***4**(1983), 324-331.

## 1982

The Steiner Problem in Phylogeny is NP-Complete, (with L.R. Foulds),

*Adv. Applied Math.***3**(1982), 43-49.On Graphs which Contain All Sparse Graphs, (with L. Babai, F.R.K. Chung, P. Erdos, and J.H. Spencer),

*Ann. Disc. Math.***12**(1982), 21-26.Linear Extensions of Partial Orders and the FKG Inequality,

*Ordered Sets*, I. Rival ed., D. Reidel Publishing Co., Boston (1982), 213-236.Tiling Rectangles with Rectangles, (with F.R.K. Chung and E.N. Gilbert, J.B. Shearer, J.H. van Lint),

*Math. Mag.***55**(1982), 286-291.Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs, (with F.R.K. Chung and P. Erdos),

*Jour. Comb. Theory (A)***32**(1982), 241-251.L'art de jongler, (with J. Buhler),

*La Recherche***13**(1982) 856-865. Give Juggling a Hand, (abridged version appeared as:)*Readers Digest*, (December, 1988), 73-76.Combinatorial Scheduling Theory, Part I,

*Chinese Journal of Operations Research***1**(1982) 36-46.On the Minimum Dominating Pair Number of a Class of Graphs, (with F.R.K. Chung, E.J. Cockayne and D.J. Miller),

*Carrib. Jour. Math.***1**(1982) 73-76.Applications of the FKG Inequality and its Relatives,

*Proc. 12th Int'l Symp. on Math. Programming*, Springer-Verlag, (1982), 115-131.Unlikelihood That Minimal Phylogenies for a Realistic Biological Study Can Be Constructed in Reasonable Computational Time, (with L.R. Foulds),

*Math. Biosciences***60**(1982), 133-142.The Fulkerson Prizes in Discrete Mathematics,

*Notices of the Amer. Math Soc.***29**(1982), 624-625.

## 1981

Fault-free Tilings of Rectangles,

*The Mathematical Gardner*, D. Klarner ed., Wadsworth, Belmont, (1981), 120-126.Monochromatic Lines in Partitions of

*Z*^N, (with W.-C.W. Li and J.L. Paul),*Lecture Notes in Math.***884**Springer-Verlag, N. Y. (1981), 35-48.On Irregularities of Distribution of Real Sequences, (with F.R.K. Chung),

*Proc. Nat. Acad. Sci., USA***78**(1981), 4001.On Trees Containing All Small Trees, (with F.R.K. Chung and D. Coppersmith),

*The Theory of Applications of Graphs*, G. Chartrand ed., John Wiley & Sons Inc., N. Y. (1981), 265-272.On The Bandwidths of a Graph and its Complement, (with P.Z. Chinn, F.R.K. Chung and P. Erdos),

*The Theory of Applications of Graphs*, G. Chartrand ed., John Wiley & Sons Inc., N.Y. (1981), 243-253 (Proc. 4th Int'l. Graph Th. Conf.).Recent Results in Graph Decompositions, (with F.R.K. Chung),

*Proc. of the 8th British Comb. Conf.*, (1981), 103-123.Efficient Realization Techniques for Network Flow Patterns, (with F.R.K. Chung, F.K. Hwang),

*Bell Sys. Tech. Jour.***60**(1981), 1771-1786.On Steiner Trees for Bounded Point Sets, (with F.R.K. Chung),

*Geometriae Dedicata***11**(1981), 353-361.On The Permanents of Complements of the Direct Sum of Identity Matrices, (with F.R.K. Chung, P. Diaconis and C.L. Mallows),

*Adv. Applied. Math.***2**(1981), 121-137.Homogeneous Collinear Sets in Partitions of

*Z*^n, (with W.-C.W. Li and J.L. Paul),*Jour. Comb. Theory (A)***31**(1981), 21-32.Minimal Decomposition of All Graphs with Equinumerous Vertices and Edges into Mutually Isomorphic Subgraphs, (with F.R.K. Chung and P. Erdos),

*Colloq. Math. Soc. Janos Bolyai, 37, Finite and Infinite Sets, Eger, Hungary (1981)*, 171-179.On Irregularities of Distribution, (with F.R.K. Chung),

*Colloq. Math. Soc. Janos Bolyai, 37, Finite and Infinite Sets, Eger, Hungary, (1981)*, 181-222.Minimal Decompositions of Graphs into Mutually Isomorphic Subgraphs, (with F.R.K. Chung and P. Erdos),

*Combinatorica***11**(1981), 13-24.**Rudiments of Ramsey Theory**,*A.M.S. Conf. Board of Math. Sciences Lect. Notes***45**, v+65 pp (Russian edition, Mir, Moscow 1984, 96 pp.) (1981).Universal Caterpillars, (with F.R.K. Chung and J. Shearer),

*J. Comb. Theory (B)***31**(1981), 348-355.The Analysis of Sequential Experiments with Feedback to Subjects, (with P. Diaconis),

*Annals of Stat.***9**(1981), 3-23.

## 1980

Information Bounds are Weak in the Shortest Distance Problem, (with A.C. Yao and F.F. Yao),

*Jour. A.C.M.***27**(1980), 428-444.On The Structure of

*t*-Designs, (with S.-Y.R. Li and W.-C.W. Li),*SIAM J. Alg. Disc. Meth.***1**(1980), 8-14.On Partitions of

*E*^*n*,*Jour. Comb. Theory (A)***28**(1980), 89-97.A Note on the Intersection Properties of Subsets of Integers, (with M. Simonovits and V.T. Sos),

*Jour. Comb. Theory (A)***28**(1980), 106-110.Lower Bounds for Constant Weight Codes, (with N.J.A. Sloane),

*IEEE Trans. of Information Th.*IT-26 (1980), 37-43.Some Monotonicity Properties of Partial Orders, (with A.C. Yao and F.F. Yao),

*SIAM Jour. Alg. Disc. Meth.***1**(1980), 251-258.On Additive Bases and Harmonious Graphs, (with N.J.A. Sloane),

*SIAM Jour. Alg. Disc. Meth.***1**(1980), 382-404.On Unimodality for Linear Extensions of Partial Orders, (with F.R.K. Chung and P.C. Fishburn),

*SIAM Jour. Alg. Disc. Meth.***1**(1980), 405-410.On a Diophantine Equation Arising in Graph Theory,

*Europ. Jour. Comb.***1**(1980), 107-112.On Bases with an Exact Order, (with P. Erdos),

*Acta Arith.***37**(1980), 201-207.**Old and New Problems and Results in Combinatorial Number Theory**, (with P. Erdos),*Mono. No. 28 de L'Enseignement Math., Univ. Geneva (1980)*128 pp.**Ramsey Theory**, (with B. Rothschild and J.H. Spencer), John Wiley and Sons, NY (1980), ix+174pp.Computational Complexity of Linear Programming,

*Science and Technology***1**(1980), 65-67. (in Chinese).

## 1979

On Universal Graphs, (with F.R.K. Chung),

*Proc. 2nd Int'l Conf. on Comb. Math.*, Annals of N.Y. Acad. Sci.,**319**(1979), 136-140.On Constant Weight Codes and Harmonious Graphs, (with N.J.A. Sloane),

*Proc. West Coast Conf. on Comb., Graph Theory, and Comp., Congressus Numerantium***26**(1979), 25-40. Also,*Utilitas Math.***26**(1980), 25-40.Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey, (with E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan),

*Annals of Dis. Math.***5**(1979), 169-231.On Properties of a Well-Known Graph or What is Your Ramsey Number?, (with T. Odda),

*Annals N.Y. Acad. Sci.***328**(1979), 166-172.A General Ramsey Product Theorem, (with J.H. Spencer),

*Proc. Amer. Math. Soc.***73**(1979), 137-139.Report of the Session on Complexity of Combinatorial Problems, (with D. Hausmann, Editorial Associate),

*Annals of Dis. Math***4**(1979), 175-176.Maximum Antichains of Rectangular Arrays, (with G.W. Peck),

*Jour. Comb. Theory (A)***27**(1979), 397-400.Minimal Decompositions of Two Graphs into Pairwise Isomorphic Subgraphs, (with F.R.K. Chung, P. Erdos, S.M. Ulam and F.F. Yao),

*Proc. 10th S-E Conf. on Comb., Graph Theory and Comp., Congressus Numerantium***23**(1979), 3-18.Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics, (with P. Erdos),

*L'Enseignement Math.***25**(1979), 325-344.On the Product of the Point and Line Covering Numbers of a Graph, (with F.R.K. Chung and P. Erdos),

*Proc. 2nd Int'l Conf. on Comb. Math., Annals of N.Y. Acad. Sci.***319**(1979), 597-602.Combinatorial designs related to the strong perfect graph conjecture, (with V. Chvatal, A.F. Perold, and S.H. Whitesides),

*Discrete Mathematics***26**(1979), 83-92.

## 1978

Spectra of Numbers, (with S. Lin and C.-S. Lin),

*Math. Mag.***51**(1978), 174-176.Ramsey Theory, (with B.L. Rothschild),

*Studies in Comb.*, G.-G. Rota ed., Math. Assoc. of Amer.,**17**(1978), 80-99.Performance Guarantees for Scheduling Algorithms, (with M.R. Garey and D.S. Johnson),

*Oper. Research*26 (1978), 3-21.On Graphs which Contain All Small Trees, (with F.R.K. Chung),

*Jour. Comb. Theory (B)***24**(1978), 14-23.Steiner Trees for Ladders, (with F.R.K. Chung),

*Annals Disc. Math.***2**(1978), 173-200.Answering Rota's Question,

*Enc. Britannica Yearbook of Science and the Future*, (1978), 537.The Combinatorial Mathematics of Scheduling,

*Scientific American***238**(1978), 124-132.The Number of Baxter Permutations, (with F.R.K. Chung, V.E. Hoggatt, Jr. and M. Kleiman),

*Jour. Comb. Theory (A)***24**(1978), 382-394.Distance Matrix Polynomials of Trees, (with L. Lovasz),

*Th. and Application of Graphs*, Lectures Notes in Math. Series, (1978), pp. 186-190. Also a French translation appears in*Colloq. Int. C.N.R.S. Problems Combinatories et Theorie des Graphs*, 189-190.Complexity Results for Bandwidth Minimization, (with M.R. Garey, D.S. Johnson, and D.E. Knuth),

*SIAM J. Appl. Math.***34**(1978), 477-495.Addition Chains with Multiplicative Cost, (with A.C.-C. Yao and F.-F. Yao),

*Disc. Math.***23**(1978), 115-119.Distance Matrix Polynomials of Trees, (with L. Lovasz),

*Adv. in Math.***29**(1978), 60-88.On Subgraph Number Independence in Trees, (with E. Szemeredi),

*Jour. Comb. Theory (B)***24**(1978), 213-222.Maximum Antichains in the Partition Lattice,

*Math. Intelligencer***1**(1978) 84-86.Combinatorial Scheduling Theory,

*Mathematics Today: Twelve Informal Essays*, Springer-Verlag, N.Y. (1978), 183-211.

## 1977

On the Distance Matrix of a Directed Graph, (with A.J. Hoffman and H. Hosoya),

*Jour. Graph Theory***1**(1977), 85-88.The Complexity of Computing Steiner Minimal Trees, (with M.R. Garey and D.S. Johnson),

*SIAM J. Appl. Math.***32**(1977), 835-859.The Limits of Computation, (with M.R. Garey),

*Encyclopedia Britannica Yearbook of Science and the Future*, (1977), 172-185.Spearman's Footrule as a Measure of Disarray, (with P. Diaconis),

*Jour. Royal Statis. Soc. Series B*,**39**(1977), 262-268.On Extremal Density Theorems for Linear Forms, (with H.S. Witsenhausen and J.H. Spencer), Number Theory and Algebra, Acad. Press, Inc., (1977), 103-109.

On Permutations Containing No Long Arithmetic Progressions, (with J.A. Davis, R.C. Entringer, and G.J. Simmons),

*Acta Arith.***34**(1977), 81-90.

## 1976

Some NP-Complete Geometric Problems, (with M.R. Garey and D.S. Johnson),

*Proc. 8th Annual ACM Symp. on Th. of Comp.*(1976), 10-22.On Graphs Which Contain All Small Trees, II, (with F.R.K. Chung and N. Pippenger),

*Colloq. Math. Soc. Janos Bolyai*,**18**(1976), 213-223.Bounds on the Performance of Scheduling Algorithms,

*Computer and Job-Shop Scheduling Theory*, E.G. Coffman, ed., John Wiley and Sons, N.Y., (1976), 165-227.On the Distance Matrix of a Tree, (with M. Edelberg and M.R. Garey),

*Disc. Math.***14**(1976), 23-39.On the Set of Distances Determined by the Union of Arithmetic Progressions, (with F.R.K. Chung),

*Ars Comb.***1**(1976), 57-76.On Addressing Graphs which Have Simple Skeletons, (with S. Chevion),

*Nanta Math.***11**(1976), 1-6.On the Permanent of Schur's Matrix, (with D.H. Lehmer),

*Jour. Australian Math. Soc.***21**(series A) (1976), 487-497.Resource Constrained Scheduling as Generalized Bin Packing, (with M.R. Garey, D.S. Johnson and A.C.-C. Yao),

*Jour. Comb. Theory (A)***21**(1976), 257-298.On the Prime Factors of ${n \choose k}$, (with P. Erdos),

*Fib. Quart.***14**(1976), 348-352.A Remark on Steiner Minimal Trees, (with F.K. Hwang),

*Bull. Inst. Math. Acad. Sinica, Taiwan***4**(1976), 177-182.On A Number-Theoretic Bin Packing Conjecture, (with M.R. Garey and D.S. Johnson),

*Colloq. Math. Soc. Janos Bolyai***18**(1976), 377-392.On Products of Factorials, (with P. Erdos),

*Bull. Inst. Math. Acad. Sinica, Taiwan***4**(1976), 337-355.

## 1975

On Cubical Graphs, (with M.R. Garey),

*Jour. Comb. Theory (B)***18**(1975), 84-95.The Largest Small Hexagon,

*Jour. Comb. Theory (A)***18**(1975), 165-170.On the prime factors of ${2n \choose n}$, (with P. Erdos, I.Z. Ruzsa and E.G. Straus),

*Math. Comp.***29**(1975), 83-92.Bounds for Multiprocessor Scheduling with Resource Constraints, (with M.R. Garey),

*SIAM J. Comp.***4**(1975), 187-200.On Multicolor Ramsey Numbers for Complete Bipartite Graphs, (with F.R.K. Chung),

*Jour. Comb. Theory (B)***18**(1975), 164-169.On Packing Squares with Equal Squares, (with P. Erdos),

*Jour. Comb. Theory (A)***19**(1975), 119-123.On Sparse Graphs with Dense Long Paths, (with P. Erdos, and E. Szemeredi),

*Comp. and Math. with Appls.***1**(1975), 365-369.Some Recent Developments in Ramsey Theory, (with B.L. Rothschild),

*Proc. NATO Advanced Study Institute on Combinatorics, Nijenrode Castle*, Math. Centre Tracts (1975), 261-276.

## 1974

A Short Proof of Van Der Waerden's Theorem on Arithmetic Progressions, (with B.L. Rothschild),

*Proc. Amer. Math. Soc.***42**(1974), 385-386.Are There

*n*+2 Points in*E^n*with Odd Integral Distances?, (with B.L. Rothschild and E.G. Straus),*Amer. Math. Monthly***81**(1974), 21-25.Performance Bounds on the Splitting Algorithm for Binary Testing, (with M.R. Garey),

*Acta Informatica***3**(1974), 347-355.Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms, (with D.S. Johnson, A. Demers, J.D. Ullman, and M.R. Garey),

*SIAM J. Comp.***3**(1974), 299-325.

## 1973

Increasing Paths in Edge Ordered Graphs, (with D.J. Kleitman),

*Periodica Math. Hungarica***3**(1-2) (1973), 141-148.Euclidean Ramsey Theorems. I, (with P. Erdos, P. Montgomery, B.L. Rothschild, J. Spencer, and E.G. Straus),

*Jour. Comb. Theory***14**(1973), 341-363.Covering the Positive Integers by Disjoint Sets of the Form {

*n*α+β:*n*=1,2,...},*Jour. Comb. Theory***15**(1973), 354-358.Euclidean Ramsey Theorems, II, (with P. Erdos, P. Montgomery, B.L. Rothschild, J. Spencer and E.G. Straus),

*Colloq. Math. Soc. Janos Bolyai***10**(1973), 529-557.On Partition Theorems for Finite Graphs, (with P. Erdos),

*Colloq. Math. Soc. Janos Bolyai***10**(1973), 515-527.Euclidean Ramsey Theorems, III, (with P. Erdos, P. Montgomery, B.L. Rothschild, J. Spencer, and E.G. Straus),

*Colloq. Math. Soc. Janos Bolyai***10**(1973), 559-583.Bounds on Scheduling with Limited Resources, (with M.R. Garey),

*Proc. 4th ACM Symp. Oper. Sys. Principles*, (1973), 104-111.An Analysis of Some Packing Algorithms, (with M.R. Garey and J.D. Ullman),

*Comb. Algorithms*, ed. R. Rustin, Algorithmic Press, (1973), 39-48.

## 1972

On a Linear Diophantine Problem of Frobenius, (with P. Erdos),

*Acta Arithmetica***21**(1972), 399-408.On Embedding Graphs in Squashed Cubes, (with H.O. Pollak),

*Graph Theory and Appl.*, Lecture Notes in Math. 303, Springer-Verlag, (1972), 99-110.Ramsey's Theorem for a Class of Categories, (with K. Leeb and B.L. Rothschild),

*Proc. of the Natl Acad. of Sci.***69**(1972), 119-120.Optimal Scheduling for Two-Processor Systems, (with E.G. Coffman, Jr.),

*Acta Informatica***1**(1972), 200-213.Bounds on Multiprocessing Anomalies and Related Packing Algorithms,

*Proc. AFIPS-Conf.***40**(1972), 205-217.Review of Principles of Combinatorics by C. Berge,

*SIAM Review***14**(1972), 344-346.On Sums of Fibonacci Numbers, (with P. Erdos),

*Fib. Quart.***10**(1972), 249-254.Complements and Transitive Closures, (with D.E. Knuth and T.S. Motzkin),

*Disc. Math.***2**(1972), 17-29.Ramsey's Theorem for a Class of Categories, (with K. Leeb and B.L. Rothschild),

*Adv. in Math.***8**(1972) 417-433. Ramsey's Theorem for a Class of Categories (Errata), (with K. Leeb and B.L. Rothschild),*Adv. in Math.***10**(1973), 326-327. Reprinted with corrections in*Classic Papers in Combinatorics*, I. Gessel and G.-C. Rota, eds. Birkhauser, Boston, (1987), 431-445.An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set,

*Info. Proc. Letters***1**(1972), 132-133.On Highly Non-Associative Groupoids, (with J.H. Folkman),

*Colloq. Math.***25**(1972), 1-10.On Tightest Packings in the Minkowski Plane, (with H.S. Witsenhausen and H.J. Zassenhaus),

*Pac. Jour. of Math.***41**(1972), 699-715.A Simpler Counterexample to the Reconstruction Conjecture for Denumerable Graphs, (with J. Fisher and F. Harary),

*Jour. Comb. Theory***12**(1972), 203-204.Worst Case Analysis of Memory Allocation Algorithms, (with M.R. Garey and J.D. Ullman),

*Proc. Fourth ACM Symp. on Th. of Comp.*, (1972) 143-150.

## 1971

On Small Graphs with Forced Monochromatic Triangles, (with J.H. Spencer),

*Recent Trends in Graph Th.*, Springer Lecture Notes in Mathematics,**86**(1971), 137-141.A Constructive Solution to a Tournament Problem, (with J.H. Spencer),

*Canad. Math. Bull.***14**(1971), 45-48.Rota's Geometric Analogue to Ramsey's Theorem, (with B.L. Rothschild),

*Proc. of Amer. Math. Soc. Symp. in Pure Math.***19**(1971), 101-104.Ramsey's Theorem for

*n*-Parameter Sets, (with B.L. Rothschild),*Trans. Amer. Math. Soc.***159**(1971), 257-292.On the Addressing Problem for Loop Switching, (with H.O. Pollak),

*Bell Sys. Tech. Jour.***50**(1971), 2495-2519.A Survey of Finite Ramsey Theorems, (with B.L. Rothschild),

*Proc. 2nd Louisiana State Univ. Conf. on Comb., Graph Th. and Comp.*, (1971), 21-40.On Sorting by Comparisons,

*Computers in No. Th., Proc. of the Sci. Res.*, (1971), 263-269.On Sums of Integers Taken from a Fixed Sequence,

*Proc. Wash. State Univ. Conf. on Number Theory*, (1971), 22-40.

## 1970

Irregularities in the Distributions of Finite Sequences, (with E.R. Berlekamp),

*Jour. Num. Th.***2**(1970), 152-161.Note on a Nonlinear Recurrence Related to √2, (with H.O. Pollak),

*Math. Mag.***43**(1970), 143-145.A Mathematical Study of a Model of Magnetic Domain Interactions,

*Bell Sys. Tech. Jour.***49**(1970), 1627-1644.On Primitive Graphs and Optimal Vertex Assignments,

*Annals. N.Y. Acad. Sci., Int. Conf. Comb. Math.*,**175**(1970), 170-186.On Subtrees of Directed Graphs with No Path of Length Exceeding One,

*Canad. Math. Bull.***13**(1970), 329-332.On a Class of Equivalent Linear and Nonlinear Integer Programming Problems, (with S.A. Burr),

*Colloq. Math. Soc. Janos Bolyai, Proc. Symp. on Comb. Th. and its Appl.*, Balatonfured (1970), 199-211.Ramsey's Theorem for

*N*-Parameter Sets: An Outline, (with B. L. Rothschild),*Colloq. Math. Soc. Janos Bolyai, Proc. Symp. on Comb. Th. and its Appl.*, Balatonfured (1970), 531-552.

## 1969

On Finite 0-Simple Semigroups and Graph Theory,

*Math. Sys. Th.***2**(1969), 325-339.Bounds on Multiprocessing Timing Anomalies,

*SIAM Jour. Appl. Math.***17**(1969), 416-429.Ramsey's Theorem for n-Dimensional Arrays, (with B.L. Rothschild),

*Bull. Amer. Math. Soc.***75**(1969), 418-422.An Irreducibility Criterion for Polynomials over the Integers, (with W.S. Brown),

*Amer. Math. Monthly***76**(1969), 795-797.Universal Single Transition Time Asynchronous State Assignments, (with A.D. Friedman and J.D. Ullman),

*IEEE Trans. on Computers*C-18 (1969), 541-547.Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications (Appendix), (with J.K. Wolf),

*Bell Sys. Tech. Jour.***48**(1969), 2405-2424.Some Results on Matching in Bipartite Graphs, (with L.H. Harper),

*SIAM Jour. Appl. Math.***17**(1969), 1017-1022.A Packing Inequality for Compact Convex Subsets of the Plane, (with J.H. Folkman),

*Canad. Math. Bull.***12**(1969), 745-752.

## 1968

On the Distribution of

*n*θ Modulo 1, (with J.H. van Lint),*Canad. Jour. of Math.***20**(1968), 1020-1024.Maximal Subsemigroups of Finite Semigroups, (with N. Graham and J. Rhodes),

*Jour. Comb. Th.***4**(1968), 203-209.An Upper Bound on the Minimum Distance for a

*k*-ary Code, (with A.D. Wyner),*Inf. and Control***13**(1968), 46-52.On Edgewise 2-Colored Graphs with Monochromatic Triangles and Containing no Complete Hexagon,

*Jour. Comb. Th.***4**(1968), 300.

## 1967

On Partitions of an Equilateral Triangle,

*Canad. Jour. of Math.***19**(1967), 394-409.On

*n*-valued Functionally Complete Truth Functions,*Jour. Symb. Logic***32**(1967), 190-195.

## 1966

On Partitions of a Finite Set,

*Jour. Comb. Th.***1**(1966), 215-223.On the Number of Information Symbols in Difference-Set Cyclic Codes, (with F.J. MacWilliams),

*Bell Sys. Tech. Jour.***45**(1966), 1057-1070.The Solution of a Certain Recurrence, (with J. Riordan),

*Amer. Math. Monthly***73**(1966), 604-608.Bounds for Certain Multiprocessing Anomalies,

*Bell Sys. Tech. Jour.***45**(1966), 1563-1581.

## 1965

On the Decomposition of Lattice-Periodic Functions,

*Bell Sys. Tech. Jour.***44**(1965), 1191-1214.

## 1964

On Finite Sums of Unit Fractions,

*Proc. London Math. Soc.***14**(1964), 193-207.On a Conjecture of Erdos in Additive Number Theory,

*Acta Arith.***10**(1964), 63-70.On Quadruples of Consecutive

*k*th Power Residues,*Proc. Amer. Math. Soc.***15**(1964), 196-197.Complete Sequences of Polynomial Values,

*Duke Math. Jour.***31**(1964), 275-286.A Property of Fibonacci Numbers,

*Fib. Quart.***2**(1964), 1-10.A Fibonacci-Like Sequence of Composite Numbers, Math. Mag., 37 (1964), 322-324.

On Finite Sums of Reciprocals of Distinct

*n*th Powers, Pac. Jour. of Math., 14 (1964), 85-92.

## 1963

On a Theorem of Uspensky,

*Amer. Math. Monthly***70**(1963), 407-409.A Theorem on Partitions,

*Jour. Australian Math. Soc.***3**(1963), 435-441.(errata)A Combinatorial Theorem for Partial Sums,

*Ann. Math. Stats.***34**(1963), 1600-1602. (erratum)