
2016present

Regularity lemmas for clustering graphs, preprint.

Permanental generating functions and sequential importance sampling
, preprint,
(with Persi Diconis and Ron Graham)

Efficient packings of unit squares in a large square
, Discrete and Computational Geometry, to appear,
(with R. Graham)

The maximum relaxation time of a random walk
,
Advances in Applied Math., 101, (2018), 114,
(with S. G. Aksoy, M. Tait and J. Tobin)

Well dispersed sequences in [0,1]^d
, J. Number Theory, 189, (2018), 124,
(with Ron Graham)

The digraph drop polynomial, in Connections in Discrete Mathematics,
(S. Butler, J. Cooper, G. Hurlbert, eds.) Cambridge University Press, 2018, 86103,
(with Ron Graham)

Sum
sequences modulo n, JCT(A), 158, (2018), 290314,
(with Jon Folkman and Ron Graham)

The drop polynomial of a weighted digraph, JCT(B), 126, (2017), 6282,
(with Ron Graham)

A semisupervised heat kernel pagerank MBO algorithm for data classification
, Comm. Math. Sci., 16 (2018), 12411264,
(with Ekaterina Merkurjev and Andrea L. Bertozzi)

The spectral gap of graphs arising from substring reversals, The Electronic J. of Combinatorics, 24, no. 3 (2017), #P.3.4,
(with J. Tobin)

A strong Harnack inequality for graphs,
Comm. Analysis and Geometry, 25, no. 3, (2017), 557588,
(with S.T. Yau).

Extreme values of the stationary distribution of random walks on directed graphs
,
Advance in Applied Math., 81, (2016), 128155,
(with Sinan Aksoy and Xing Peng).

A generalized AlonBoppana bound and weak Ramanujan graphs, Electronic Journal of Combinatorics, 23, (2016), Paper #3.4, (20 pages).
The
version in EJC.

On the discrepancy of circular sequences of reals, J. Number Theory, 164 (2016), 5265,
(with R. L. Graham).

Curvature aspects of graphs,
Proc. of AMS, 145 (2017), 20332042,
(with F. Bauer, Y. Lin and Y. Liu).

Decomposition of random graphs into complete bipartite graphs , SIAM J. Discrete Math., 30, no. 1, (2016), 296310,
(with X. Peng).

Worstcase analysis of the LPT algorithm for single processor scheduling with time restrictions, OR Spectrum, 38(2), (2016), 531540,
(with O. Braun and R. L. Graham).

The matrix cover polynomial,
J. Combinatorics, 7 (2016), 375412,
(with R. L. Graham).
20112015
 Distributed algorithms for finding local clusters using heat kernel pagerank, WAW, 2015,
LNCS 9479, Springer, 177189,
(with O. Simpson).

A brief survey of PageRank algorithms,
IEEE Transactions on Network Science and Engineering, 1, No. 1, (2015), 3842.

Edge flipping in the complete graphs, Advances in Appl. Math. 69 (2015), 4664,
(with S. Butler, J. Cummings and R. L. Graham).

Computing heat kernel pagerank and a local clustering algorithms,
Combinatorial Algorithms, Lecture Notes in Comput. Sci., 8986, Springer, Cham, 2015, 110121,
and the journal version appears in European Journal of Combinatorics, 68 (2018), 96119,
(with O. Simpson).

Discrepancy inequalities for directed graphs
,
Discrete Applied Mathematics, 176 (2014) 3042,
(with F. Kenter).

Complex Networks, a chapter in Handbook of Graph Theory, (eds. J. L. Gross et. al), 14561476, CRC Press, 2014,
(with A. Bonato).

Harnack inequalities for graphs with nonnegative Ricci curvature
,
J. Math. Anal. Appl. 415 (2014), 25  32,
(with Yong Lin and S.T. Yau).

A chapter titled ``Spectral Graph Theory", to appear in Handbook of Linear Algebra, CCR Press,
(with Steve Butler).

A note on an alternating upper bound for random walks on semigroups
,
Discrete Applied Mathematics,
176 (2014), 2429,
(with J. Hughes).

Single processor scheduling with time restrictions,
J. of Scheduling, 17 (2014), 399403,
(with O. Braun and R. Graham).

From quasirandom graphs to graph limits and graphlets
,
Advances in Applied Math. 56 (2014),
135174.

Solving linear systems with boundary conditions using heat kernel pagerank
WAW 2013, LNCS 8305, 203219,
(with Olivia Simpson).
The journal version appeared in Internet Mathematics, 11 (2015), 449471.

A local clustering algorithm for connection graphs
,
WAW 2013, LNCS 8305, 203219,
(with Mark Kempton).
The journal version appeared in Internet Math., 11 (2015), 333351.

Inversiondescent polynomials for restricted permutations,
J. of Combinatorial Theory, A, 120, (2013), 366378,
(with Ron Graham).

Spectral clustering of graphs with general degrees in the extended planted partition model
,
COLT 2012,
Journal of Machine Learning Research, (2012), 123,
(with K. Chaudhuri and A. Tsiatas).

Ranking and sparsifying a connection graph,
WAW 2012,
LNCS 7323 (2012), 6677,
(with M. Kempton and W. Zhao).
The journal version appeared in Internet Mathematics, 10 (2014), 87115.

Generalized Euler sums,
Journal of Combinatorics, 3, (2012), 299316,
(with Ron Graham).

Multicommodity allocation for dynamic demands using PageRank vectors
,
WAW2012,
LNCS 7323 (2012), 138152,
(with P. Horn and J. Hughes).
The journal version appeared in Internet Mathematics, 10 (2014), 4965.

Braess's paradox in expanders
,
Random Structures and Algorithms, 41 (2012), 451468,
(with S. J. Young and W. Zhao).

Hypergraph coloring games and voter models
,
WAW2012, LNCS 7323 (2012), 116,
(with Alex Tsiatas).
The
journal version appeared in Internet Mathematics, 10 (2014), 6686.

Edge flipping in graphs,
Advances in Applied Mathematics, 48 (2012) 3763,
(with Ron Graham).

Diameter
of random spanning trees in a given graph ,
Journal of Graph Theory,
69, (2012), 223240,
(with P. Horn and L. Lu).

Dirichlet PageRank and trustbased ranking algorithms,
WAW 2011, LNCS 6732, (2011), 103114,
(with A. Tsiatas and Wensong Xu).
The journal version,
Dirichlet PageRank and
ranking algorithms based on trust and distrust,
appeared in Internet Mathematics, 9, (2013), 113134.

On the spectra of general random graphs,
Electronic Journal of Combinatorics, 18(1),
(2011), P215, 14 pages,
(with M. Radcliffe).
20062010
Back to top

Graph Theory in the information age
,
Notices of AMS, 57, no. 6, July 2010, 726732.
This article was translated into Chinese and appeared in
Mathematical Advances in Translation, 3, 2010, 207213.

A symmetric
Eulerian identity
,
Journal of Combinatorics, 1 (2010), 2938,
(with Ron Graham and Don Knuth).

PageRank and random walks on graphs
,
Fete of Combinatorics and Computer Science, (G. O. H. Katona, A. Schrijver and T. Szonyi, Eds.),
Springer, Berlin, (2010), 4362,
(with Wenbo Zhao).

Small
spectral gap in the combinatorial Laplacian implies Hamiltonian,
Annals of Combinatorics, 13, (2010), 403412,
(with S. Butler).

Tiling polygons with lattice triangles
,
Discrete and Computational Geometry, 44, (2010), 898
903,
(with Steve Butler, Ron Graham and Mikl'os Laczkovich).

Descent
polynomials for permutations with bounded drop size
,
European J. Combinatorics, 31, (2010), 18531867,
(with Anders Claesson, Mark Dukes, and Ronald Graham).

Finding and visualizing graph clusters using PageRank optimization,
WAW 2010, LNCS 6516, (2010), 8697,
(with A. Tsiatas).
The journal version appeared in Internet Mathematics, 8 (2012), 4672,
(with A. Tsiatas).

Braess's paradox in large sparse graphs,
WINE 2010, LNCS 6484, 194208,
(with Stephen J. Young).

A sharp PageRank algorithm with applications to edge ranking and graph sparsification
WAW 2010, LNCS 6516, 214,
(with Wenbo Zhao).

PageRank
as a discrete Green's function,
Geometry and Analysis, I, ALM 17, (2010), 285302.

A local graph
partitioning algorithm using heat kernel pagerank,
WAW 2009,
LNCS 5427, (2009), 6275.

Distributing antidote using PageRank vectors
,
Internet Mathematics, 6, (2009), 237254,
(with Paul Horn and Alexander Tsiatas).

The giant component
in a random subgraph of a given graph
,
Proceedings of WAW2009, Lecture Notes in Computer Science 5427, 3849,
(with P. Horn and L. Lu).

Packing equal squares into a large square
,
JCT(A), 116, (2009), 11671175,
(with R. L. Graham).

A whirlwind tour of random graphs
,
a survey article in Encyclopedia on Complex Systems, Springer, 2008.

A network color game
,
WINE 2008, Lecture Notes in Computer Science, Volume 5385 (2008), 522530,
(with K. Chaudhuri and M. S. Jamall).

Quasirandom graphs with
given degree sequences,
Random Structures and Algorithms, 12 (2008), 119,
(with R. L. Graham).

Primitive juggling sequences,
Amer. Math. Monthly, 115, March 2008, 185194,
(with Ron Graham).

Four
Cheegertype inequalities for graph
partitioning algorithms
,
Proceedings of ICCM, II, (2007), 751772.

The heat kernel as the pagerank of a graph
,
PNAS, 105 (50), (2007), 1973519740.

Local partitioning for directed graphs using PageRank
,
WAW2007, 166178,
(with R. Andersen and Kevin Lang).
The full paper is in Internet Mathematics, 5 (2008), 322.

The
spectral gap of a random subgraph of a graph,
the
extended abstract appeared in Proceedings of WAW2006, LNCS 4937 and the complete version is in Internet Math, 4 (2007), 225244,
(with Paul Horn).

Parallelism versus memory allocation in pipelined router
forwarding engines,
Theory Comput. Systems 39 (2006), 829849,
(with R. Graham, J. Mao and G. Varghese).

Detecting sharp
drops in PageRank and a simplified local partitioning algorithm
Theory and Applications of Models of Computation,
Proceedings of TAMC 2007, LNCS 4484, Springer, (2007), 112,
(with R. Andersen).

Local
graph partitioning using pagerank vectors,
FOCS 2006, 475486,
(with R. Andersen and K. Lang).
The full paper version,
Using pagerank vectors to locally partition a graph appeared in Internet Mathematics, 4 (2007), 3564.

Random walks and local cuts
in graphs,
Linear Algebra and its Applications, 423 (2007), 2232.

Universal juggling cycles,
Integers,
Combinatorial Number Theory, B.
Landman, M.B. Nathanson, J. Nesetril, R.J. Nowakowski, C. Pomerance, eds.
(2007), 121130. Also appeared in INTEGERS 7(2) (2007), A8 (electronic) 10
pp.
(with Ron Graham).

Weighted Laplacians and the Sigma function of a graph,
Quantum Graphs and their Applications,
(B. Berkolaiko et. al. eds), Contemporary Math., AMS, Providence, RI,
93107, 2006
(with Ross Richardson).
 Oblivious and adaptive strategies for the majority and plurality problems,
Algorithmica, 48 (2007), 147157,
(with R. Graham, Jia Mao and Andrew Yao)

Concentration
inequalities and martingale inequalities  a survey,
Internet Math.,
3 (20062007), 79127,
(with L. Lu).

Maximizing data locality in distributed systems,
Journal of Computer System Sciences, 72 (December 2006),
13091316,
(with Ronald Graham, Ranjita Bhagwan, Stefan Savage and Geoffrey M. Voelker).

The volume of the giant component of a
random graph with given expected degrees,
SIAM J. Discrete Math. 20 (2006), no. 2, 395411,
(with L. Lu).

A brief overview of network algorithms,
J. of Computer and System Sciences 72 (2006), no. 3, 420424.

The diameter and
Laplacian eigenvalues of directed graphs,
Electronic Journal of Combinatorics 13 (2006), N4, 6 pp.

Complex Graphs and Networks,
CBMS Number 107, AMS Publications, 2006, vii+264pp.,
(with L. Lu)
20012005
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Laplacians
and the Cheeger inequality for
directed graphs,
Annals of Combinatorics, 9 (2005), 119.
 Oblivious strategies for the majority and plurality problems,
Computing and Combinatorics, Lecture Notes in Computer Science, Springer, Berlin (2005), 329338,
(with R. Graham, Jia Mao and Andrew Yao).
The journal version appeared in Algorithmica 48 (2007), 147157.

A spectral Turán theorem,
Combinatorics, Probability and Computing 14 (2005), 755767.

Drawing power law graphs,
Proceedings Graph Drawing, New York, 2004, 1217,
(with Reid Andersen, L. Lu).
Paper version, Drawing power law graphs
using a local/global decomposition, appeared in Algorithmica
47 (2007), 379397.

Analyzing
the small world phenomenon using a hybrid model with local network flow,
WAW 2004, Rome, Italy, Lecture Notes in Computer Science,
3234, Springer, 2004, 1930,
a long version appeared as
Modeling the smallworld phenomenon with local network flow,
Internet Mathematics 2 (2006), no. 3, 359385,
(with Reid Andersen, L. Lu).
 Guessing secrets with inner product questions,
Proceedings of the 13th ACMSIAM Symposium on Discrete Algorithms, (2002), 247253,
long version appeared in Internet Math., 1 (2004), no. 2, 177192,
(with R.L. Graham and Linyuan Lu).

Parallelism versus Memory Allocation
in Pipelined Router Forwarding Engines,
SPAA'04, Barcelona, Spain, (2004), 103111,
(with Ronald Graham and George Varghese).

De Bruijn cycles for covering codes,
Random Structures and Algorithms, 25, (2004), 421431,
(with J. Cooper).

Coupling online and offline analyses for random power law graphs,
Internet Mathematics, 1 (2004), 409461,
(with Lincoln Lu).

Discrete isoperimetric inequalities,
Surveys in Differential Geometry IX, International Press, (2004), 5382.

On disjoint path pairs with wavelength continuity constraint in WDM networks,
INFOCOM, 2004,
(with Reid Andersen, Arunabha Sen and Guoliang Xue).

The small world phenomenon in hybrid power law graphs,
Complex Networks, (Eds. E. BenNaim et. al.), SpringerVerlag, (2004), 89104,
(with Lincoln Lu).

Generalizations of Polya's urn problem,
Annals of Combinatorics 7 (2003), 141153,
(with Shirin Handjani and Doug Jungreis).
 Finding Favorites,
Electronic Colloquium on Computational Complexity, Report No. 78 (2003),
(with Ron Graham, Jia Mao and Andrew Yao).

Eigenvalues of random power law graphs,
Annals of Combinatorics 7 (2003), 2133,
(with Lincoln Lu and Van Vu).

The spectra of random graphs with given expected degrees,
short version,
Proceedings of National Academy of Sciences 100, no. 11, (2003), 63136318,
long version
(with full proofs) Internet Mathematics 1 (2004), 257275,
(with Lincoln Lu and Van Vu).

Duplication models for biological networks,
Journal of Computational Biology 10, no. 5, (2003), 677688,
(with Lincoln Lu, Gregory Dewey, David J. Galas).

The average distances in random graphs with given expected degrees,
abstract,
paper (short version),
Proc. National Academy of Sciences 99, no. 25, (December, 2002), 1587915882,
paper (long version)
,
Internet Mathematics 1 (2003), 91113,
(with L. Lu).

Spectral Partitioning with Indefinite Kernels using the Nyström Extension,
European Conference on Computer Vision, 2002, III, 531542.
Paper version:
Spectral grouping using the Nyström method,
IEEE Transactions on Pattern Analysis and Machine Intelligence
26, No. 2, (2004), 214225,
(with Charless Fowlkes, Serge Belongie, and Jitendra Malik).

Sparse quasirandom graphs,
abstract,
Combinatorica 22 (2002), 217244,
(with Ronald Graham)

Connected components in random graphs with given expected degree sequences,
abstract,
Annals of Combinatorics 6 (2002), 125145,
(with L. Lu).

Random evolution of massive graphs,
abstract,
Handbook of Massive Data Sets, (Eds. James Abello et al.), Kluwer Academic
Publishers, (2002), 97122,
extended abstract appeared in FOCS 2001, 510519,
(with W. Aiello and L. Lu).

On sparse sets hitting linear forms,
abstract,
Number Theory for the Millennium I,
(Eds. M. A. Bennett et al.), AK Peters, Natick, Massachusetts, (2002), 257272.
(with Paul Erdös and Ronald Graham)

A chipfiring game and Dirichlet eigenvalues,
abstract,
Discrete Math 257 (2002), 341355,
(with Robert Ellis).

Guessing secrets,
abstract,
Electronic Journal of Combinatorics 8 (2001), R13, 25 pp,
extended
abstract appeared in
Proceedings of the Twelfth Annual ACMSIAM Symposium on Discrete Algorithms
(Washington, DC, 2001), SIAM, Philadelphia, 723726,
(with Ron Graham and Tom Leighton).
also, SODA'01, 723726,
(with Ronald Graham and F. Tom Leighton).

Combinatorics for the East model,
abstract,
Advances in Applied Math. 27 (2001), 192206,
(with Persi Diaconis and Ronald Graham).

Distance realization problems with applications to Internet tomography,
J. Computer and System Sciences 63 No. 3, (November 2001), 432448,
(with Mark Garrett, Ronald Graham and David Shallcross).

The diameter of sparse random graphs,
abstract,
Advances in Applied Math. 26 (2001), 257279,
(with Linyuan Lu).

Dynamic location problems with limited lookahead,
Theoretical Computer Science 261 (2001), 213226,
(with Ron Graham).

Augmented ring networks,
IEEE Transactions on Parallel and Distributed Systems 12 (2001), 598609,
(with W. Aiello, S. N. Bhatt, A. L. Rosenberg and R. K. Sitaraman).
19962000
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Discrete Green's functions,
abstract,
J. Combinatorial Theory (A) 91 (2000), 191214,
(with S.T. Yau).

Higher eigenvalues and isoperimetric inequalities on
Riemannian manifolds and graphs,
Communications on Analysis and Geometry 8, (2000), 9691026,
(with A. Grigor'yan and S.T. Yau).

A random graph model for massive graphs,
abstract,
Proceedings of the
Thirtysecond Annual ACM Symposium on Theory of Computing
(2000),
171180,
(with Bill Aiello and Linyuan Lu).
The complete paper version
has a different title
A random graph model for power law graphs,
Experimental Math. 10 (2001), 5366.

On polynomials of spanning trees,
abstract,
Annals of Combinatorics 4 (2000), 1326,
(with C. Yang).

Weighted graph Laplacians and isoperimetric inequalities,
Pacific Journal of Mathematics 192 (2000), 257273,
(with Kevin Oden).

A Harnack inequality for Dirichlet eigenvalues,
Journal of Graph Theory, 34 (2000), 247257,
(with S.T. Yau).

Spanning trees in subgraphs of lattices,
Comtempory Math. 245, Amer. Math. Soc., Providence, R. I., 1999, 201219.

The maximum upper density of a set of positive real numbers with no solution
s
to x+y=kz,
in Paul Erdos and his mathematics (Budapest, 1999), Janos Bolyai Math. Soc.,
Budapest, 1999, 5456,
(with John L. Goldwasser).

An upper bound for the Turan number t_{3}(n,4),
Journal of Combinatorial Theory (A) 87 (1999), 381389,
(with Linyuan Lu).

Coverings, heat kernels and spanning trees,
Electronic Journal of Combinatorics 6 (1999), R12, 21 pp,
(with S.T. Yau).

Multidiameters and multiplicities,
European Journal of Combinatorics 20 (1999), 629640,
(with C. Delorme and P. Sol'e).

Logarithmic Sobolev techniques for random walks on graphs,
Emerging Applications of Number Theory, IMA Volumes in Math. and its Applications
109 (eds. D. A. Hejhal et. al.), 175186, Springer, 1999.

Forced convex ngons in the plane,
Discrete and Computational Geometry 19 (1998), 367371,
(with R.L. Graham).
 Isoperimetric inequalities for Cartesian products of graphs,
Combinatorics, Probability and Computing 7 (1998), 141148,
(with Prasad Tetali).

Erdos on Graphs. His Legacy of Unsolved Problems,
A. K. Peters, Wellesley, MA, 1998, xiv+142 pp.,
(with Ron Graham).

Open problems of Paul Erdos in graph theory,
Journal of Graph Theory 25 (1997), 336.
More

Spectral Graph Theory, (first four chapter)
CBMS Number 92, AMS Publications, 1997, xii+207 pp.

Stratified random walks on an ncube,
Random Structures and Algorithms 11 (1997), 199222,
(with R.L. Graham).

Random walks on generating sets of groups,
Electronic Journal of Combinatorics 4 no. 2, (1997) #R7, 14 pp,
(with R. L. Graham).

Eigenvalue inequalities for graphs and convex subgraphs,
Communications on Analysis and Geometry 5 (1997), 575623,
(with S.T. Yau).

On optimal strategies for cyclestealing in networks of workstations,
IEEE Trans. on Computers 46 (1997), 545557,
(with S. Bhatt, F. T. Leighton, and A. L. Rosenberg).

Integer sets containing no solutions to x+y=3z,
in The Mathematics of Paul Erdos, Springer Verlag, Berlin (1997), 218227,
(with John L. Goldwasser).

A combinatorial trace formula,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 107116,
(with S.T. Yau)

Eigenvalues and diameters for manifolds and graphs,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 79106,
(with A. Grigor'yan and S.T. Yau).

Logarithmic Harnack inequalities,
Mathematical Research Letters 3 (1996), 793812,
(with S.T. Yau).

Laplacians of graphs and Cheeger's inequalities,
in Combinatorics, Paul Erdos is eighty, Vol. 2 (Keszthely, 1993),
Bolyai Math.
Soc., Budapest, 1996, 157172.

Optical wavelength routing, translation, and packet/cell switched networks,
Journal of Lightwave Technology 14, Issue 3, March 1996, 336343,
(with Krishna Bala and Charles A. Brackett).

Maximum subsets of $(0,1]$ with no solutions to $x+y=kz$,
Electronic Journal of Combinatorics 3 (1996) R1, 23 pp,
(with John L. Goldwasser).

A combinatorial Laplacian with vertex weights,
Journal of Combinatorial Theory (A) 75 (1996), 316327,
(with R. P. Langlands).

Optimal emulations by butterflylike networks,
JACM 43 (1996), 293330,
(with S. Bhatt, JiaWei Hong, F. T. Leighton, Bojana Obrenic, A. L. Rosenberg and E.J. Schwabe).

Upper bounds for eigenvalues of the discrete and continuous
Laplace operators,
Advances in Mathematics 117 (1996) 165178,
(with A. Grigor'yan and S.T. Yau).

On sampling with Markov chains,
Random Structures and Algorithms 9 (1996) 5577.
(with R. L. Graham and S. T. Yau).

Scheduling treedags using FIFO queues: A controlmemory tradeoff,
Journal of Parallel and Distributed Computing 33 (1996), 5568,
(with Sandeep N. Bhatt, Tom Leighton and Arny Rosenberg).
19911995
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Pebbling a chessboard,
Amer. Math. Monthly 102 (1995), 113123,
(with Ron Graham, John Morrison and Andrew Odlyzko).

A Harnack inequality for homogeneous graphs and subgraphs,
Communications on Analysis and Geometry 2
(1994), 627640,
also in Turkish J. Math. 19 (1995), 273290,
(with S.T. Yau).

Eigenvalues of graphs,
Proceedings of the International Congress of Mathematicians (Zurich, 1994),
Birkhäuser Verlag, Berlin, 13331342.

Eigenvalues of graphs and Sobolev inequalities,
Combinatorics, Probability and Computing 4 (1995), 1126,
(with S.T. Yau).

Salvage embeddings of complete trees,
SIAM J. Discrete Math. 8 (1995), 617637,
(with S. Bhatt, F. T. Leighton, and A. L. Rosenberg).

On the cover polynomial of a digraph,
J. Combinatorial Theory (B) 65 (1995), 273290,
(with R. L. Graham).

Groups and the Buckyball,
in Lie Theory and Geometry: In honor of Bertram Kostant (Eds. J.L. Brylinski, R. Brylinski, V. Guillemin and V. Kac)
PM 123, Birkhäuser, Boston, 1994, 97126,
(with Bertram Kostant and Shlomo Sternberg).

Routing permutations on graphs via matchings,
SIAM J. Discrete Math. 7 (1994) 513530,
(with Noga Alon and R. L. Graham).

Chordal completions of planar graphs,
J. of Comb. Th. (B) 62 (1994), 96106,
(with David Mumford).

A report on reliable software and communication,
Bellcore Internal Memorandom 1992.
Paper version titled "Reliable software and communication: An overview",
IEEE J. Selected Areas Comm. 12, no. 1 (1994), 2332.

An upper bound on the diameter
of a graph from eigenvalues associated with its Laplacian,
SIAM J. Discrete Math. 7 (1994), 443457,
(with V. Faber and Thomas A. Manteuffel).

Several generalizations of Weil's sums,
J. of Number Theory 49 (1994) 95106.

Even cycles in directed graphs,
SIAM J. Discrete Math. 7 (1994) 474483,
(with Wayne Goddard and D. J. Kleitman).

Communication complexity and quasirandomness,
SIAM J. Discrete Math. 6 (1993), 110123,
(with Prasad Tetali)

The Laplacian of a hypergraph,
in Expanding graphs (Princeton, NY, 1992),
DIMACS Ser. Discrete Math. Theoret.
Comput. Sci., 10, Amer. Math. Soc., Providence, RI, 1993, 2136.

Chordal completions of grids and planar graphs,
in Planar graphs (New Brunswick, NJ, 1991), DIMACS Ser. Discrete Math. Theoret.
Comput. Sci., 9, Amer. Math. Soc., Providence, RI, 1993, 3740,
(with D. Mumford).

On hypergraphs having evenly distributed subhypergraphs,
Disc. Math. 111 (1993), 125129,
(with Ron Graham).

A note on constructive lower bounds for the Ramsey numbers R(3,t),
J. Comb. Theory (B) 57 (1993), 150155,
(with R. Cleve and P. Dagum).

Mathematics and the Buckyball,
(this is a somewhat different version from the one
that appeared in American Scientist 81, No. 1., (1993) 5671),
(with Shlomo Sternberg).
 The number of
different distances determined by a set of points in the Euclidean place,
Discrete and Computational Geometry 7 (1992), 111,
(with E. Szemeredi and W.T. Trotter).

Tolerating faults in synchronization networks,
Parallel processing: CONPAR 92VAPP V (Lyon, 1992), Lecture Notes in
Comput. Sci., 634, Springer, Berlin, 1992, 112,
(with S. N. Bhatt, F. T. Leighton and A. L. Rosenberg).

Quasiransom
subsets of Z_{n},
J. Comb. Theory (A) 61 (1992), 6486,
(with R. L. Graham).

Laplacian and vibrational spectra for homogeneous graphs,
J. Graph Theory 16 (1992), 605627,
(with Shlomo Sternberg).

Cohomological aspects of hypergraphs,
Trans. Amer. Math. Soc. 334 (1992), 365388,
(with R. L. Graham).

Universal cycles for combinatorial structures,
Discrete Math. 110 (1992), 4359,
(with P. Diaconis and R. L. Graham).

Efficient embeddings of trees in hypercubes,
SIAM Journal on Computing 21 (1992), 151162,
(with S. Bhatt, F. T. Leighton and A. Rosenberg)

Subgraphs of a hypercube containing no small even cycles,
J. Graph Theory 16 (1992), 273286.

Graphs with small diameter after edge deletion,
Discrete Applied Math. 37/38 (1992), 7394.

Maximum cuts and quasirandom graphs,
in Random Graphs, John Wiley and Sons (1992), 2333,
(with R.L. Graham).

Quasirandom set systems,
J. Amer. Math. Soc. 4 (1991), 151196,
(with R. L. Graham).

Constructing randomlike graphs,
Probabilistic Combinatorics and Its Applications, (B. Bollobas ed.), Amer. Math. Soc., Providence, (1991), 2155.

Quasirandom tournaments,
J. of Graph Theory 15 (1991), 173198,
(with R.L. Graham).

A note on finding a strict saddlepoint,
Amer. Math. Monthly 98 (1991), 418419,
(with Daniel Bienstock, Michael Fredman, Alejandro A. Schaffer, Peter W. Shor and Subhash Suri).

Improved separators for planar graphs,
Graph Theory, Combinatorics, and Applications, John Wiley and Sons, (1991), 265270.

Regularity lemmas for hypergraphs and quasirandomness,
Random Structures and Algorithms 2 (1991), 241252.
19861990
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Quasirandom classes of hypergraphs,
Random Structures and Algorithms 1 (1990), 363382.
Corrigendum.

On graphs not containing prescribed induced subgraphs,
in A Tribute to Paul Erdos, Cambridge University Press (1990), 111120,
(with R.L. Graham).

The Maximum number of edges in 2K_{2}free graphs of bounded degree,
Discrete Math. 81 (1990), 129135,
(with A. Gyarfas, W. T. Trotter and Z. Tuza).

Universal graphs and induceduniversal graphs,
J. Graph Theory 14 (1990) 443454.

Separator theorems and their applications,
Paths, Flows and VLSILayout, SpringerVerlag, Berlin (1990), 1734.

Quasirandom graphs,
a short
version appeared in Proc. Natl. Acad. Sci. USA, 85 (1988), 969970,
a long
version
appeared in Combinatorica 9 (1989), 345362,
(with R. L. Graham and R. M. Wilson).

Quasirandom hypergraphs,
Proc. Natl. Acad. Sci. USA 86 (1989), 81758177,
Long
version appeared in Random Structures
and Algorithms 1 (1990), 105124,
(with R.L. Graham).

Pebbling in hypercubes,
SIAM J. Disc. Math. 2 (1989), 467472.

Sphereandpoint incidence relations in
high dimensions with applications to unit distances and furthestneighbor pairs,
Discrete & Computational Geometry 4 (1989), 183190.

Diameters and eigenvalues,
J. of the Amer. Math. Soc. 2 (1989), 187196.

Graphs with small bandwidth and cutwidth,
Discrete Math. 75 (1989), 113119,
(with P.D. Seymour).

Optical orthogonal codes: design, analysis and applications,
IEEE Trans. on Information Theory 35, No. 3, (1989), 595604,
(with J. Salehi and V. Wei).
Erratum.

A dynamic location problem for graphs,
Combinatorica 9 (1989), 111131,
(with R. L. Graham and M. Saks).

Universal graphs for
boundeddegree trees and planar graphs,
SIAM J. Discrete Math. 2 (1989), 145155,
(with S. Bhatt, F. T. Leighton and A. L. Rosenberg).

Steiner trees on a checkerboard,
Math. Magazine 62 (1989), 8396,
(with Martin Gardner and R. L. Graham).

On the fractional covering number of hypergraphs,
SIAM J. on Discrete Math. 1 (1988), 4549,
(with Z. Furedi, M. R. Garey and R. L. Graham).

Optimal simulations by butterfly networks,
Proc. of the Twentieth Annual ACM Symposium on Theory of Computing, (1988), 192204,
(with S. N. Bhatt, JiaWei Hong, F. T. Leighton and A. L. Rosenberg).

On induced subgraphs of the cube,
J. Comb. Th. (A) 49 (1988), 180187,
(with Z. Furedi, R.L. Graham and P. Seymour).

The average distance and the independence number,
J. Graph Theory 12 (1988), 229235.

Pursuitevasion games on graphs,
J. Graph Theory 12 (1988), no. 2, 159167,
(with J.E. Cohen and R.L. Graham).

Labelings of graphs,
Selected Topics in Graph Theory 3, Academic Press, San Diego, CA, 1988, 151168.

Explicit construction of linear sized tolerant networks,
Discrete Math. 72 (1988), 1519,
(with N. Alon).

The diameter of a cycle plus a random matching,
SIAM J. on Discrete Math. 1 (1988), 328333.
(with B. Bollobás)

The maximum number of edges in a 3graph not containing a given star,
Graphs and Combinatorics 3 (1987), 111126,
(with P. Frankl).

Diameters of graphs:
old problems and new results,
Congressus Numerantium 60 (1987), 295317.

Dynamic search in graphs,
Discrete Algorithms and Complexity (1987), 351387,
(with R. L. Graham and M. Saks).

Highly irregular graphs,
J. Graph Theory 11 (1987), 235249,
(with Yousef Alavi, Gary Chartrand, Paul Erdos, R. L. Graham and Ortrud R. Oellermann).

Random walks arising in random number generation,
Ann. Probab. 15 (1987), no. 3, 11481165,
(with P. Diaconis and R.L. Graham).

On unavoidable hypergraphs,
J. Graph Theory 11 (1987), 251263,
(with P. Erdos).

Embedding graphs in books: a layout
problem with applications to VLSI design,
SIAM J. Algebraic Discrete Methods 8 (1987), no. 1, 3358,
also in
Graph theory with applications
to algorithms and computer science (Kalamazoo, Mich., 1984), 175188,
WileyIntersci. Publ., Wiley, New York, 1985,
(with F.T. Leighton and A.L. Rosenberg).

The forwarding index of communication networks,
IEEE Trans. Inform. Theory 33 (1987), no. 2, 224232,
(with E.G. Coffman, Jr., M.I. Reiman, and B.E. Simon).

Monotone subsequences in (0,1)matrices,
Graphs Combin. 2 (1986), no. 1, 3136,
(with P.C. Fishburn and V.K. Wei).

The relationship between switch capacity
and network capacity in packet switched networks,
Bell Laboratories Internal Memorandum, 1986,
(with R.R.Goldberg).

Some intersection theorems for ordered sets
and graphs,
J. Combin. Theory Ser. (A) 43 (1986), no. 1, 2337,
(with R.L. Graham, P. Frankl, and J.B. Shearer).

Optimal simulations of tree machines,
27th Annual Symposium on Foundations of Computer Science (1986), 274282,
(with S. N. Bhatt, F. T. Leighton and A. L. Rosenberg).

Minced trees, with applications to faulttolerant VLSI processor arrays,
Math. Systems Theory 19 (1986), 112,
(with A. L. Rosenberg).

Partitioning circuits for improved testability,
4th MIT Conf. on Advanced Research in VLSI,
(C. E. Leiserson, ed.), The MIT Press, Cambridge
(1986), 91106,
(with S. N. Bhatt, A. L. Rosenberg).
19811985
Back to top

Selforganizing sequential search and Hilbert's inequalities
Proceedings of the Seventeenth Annual
ACM Symposium on Theory of Computing 8 (1985), 217223,
also in J. Comp. System Sc. 36 (1988), 148157,
(with D. J. Hajela and P. D. Seymour).

On the addressing problem for directed graphs,
Graphs Combin. 1 (1985), no. 1, 4150, (with R.L. Graham, and P.M. Winkler).

Strongly connected orientations of mixed multigraphs,
Networks 15 (1985), no. 4, 477484, (with M.R. Garey and R.E. Tarjan).

Crossmonotone subsequences,
Order 1 (1985), no. 4, 351369, (with P.C. Fishburn and V.K. Wei).

Extremal subgraphs for two graphs,
J. Combin. Theory (B) 38 (1985), no. 3, 248260, (with P. Erdös and J. Spencer).

Coding strings by pairs of strings,
SIAM J. Algebraic Discrete Methods 6 (1985), no. 3, 445461,
also in Proceedings of the fourteenth Southeastern conference on combinatorics, graph theory
and computing (Boca Raton, Fla., 1983) Congr. Numer. 39 (1983), 183191,
(with R.E. Tarjan, W.J. Paul, and R. Reischuk).

Quantitative forms of a theorem of Hilbert,
J. Combin. Theory Ser. (A) 38 (1985), no. 2, 210216,
(with T.C. Brown, P. Erdös, and R.L. Graham).

On the cutwidth and the topological
bandwidth of a tree,
SIAM J. Algebraic Discrete Methods 6 (1985), no. 2, 268277.

The number of different distances determined
by n points in the plane,
J. Combin. Theory Ser. (A) 36 (1984), no. 3, 342354.

On optimal linear arrangements of trees,
Computers and Mathematics with Applications 10 (1984), 4360.

Increasing sequences with nonzero
block sums and increasing paths in edgeordered graphs,
Discrete Math. 50 (1984), no. 1, 1528, (with A. R. Calderbank and D. Sturtevant).

Diameter bounds for altered graphs,
J. Graph Theory 8 (1984), no. 4, 511534, (with M. R. Garey).

Applications of topological electroncounting
theory to polyhedral metal clusters,
Organic Chemistry 23 (1984), 12571266,
(with B.K. Teo and G. Longoni).

Diameters of communication networks,
Mathematics of information processing (Louisville, Ky., 1984), 118, Proc. Sympos.
Appl. Math. 34 Amer. Math. Soc., Providence, RI, 1986.

A survey of bounds for classical Ramsey numbers,
J. Graph Theory 7 (1983), no. 1, 2537, (with C.M. Grinstead)

Perfect storage representations for families
of data structures,
SIAM J. Algebraic Discrete Methods 4 (1983), no. 4, 548565,
(with A.L. Rosenberg and Lawrence Snyder).

Diogenes: A methodology for designing faulttolerant
VLSI processor arrays,
FTCS 13th Annual International Symposium FaultTolerant Computing (1983), 2632,
(with F.T. Leighton and A.L.Rosenberg).

On unavoidable graphs,
Combinatorica 3 (1983), no. 2, 167176, (with P. Erdös).

Unavoidable stars in 3graphs,
J. Combin. Theory Ser. (A) 35 (1983), no. 3, 252262.

On universal graphs for spanning trees,
Journal of London Math. Soc. 27 (1983), 203211
(with R. L. Graham).

Edgecolored complete graphs with precisely colored subgraphs,
Combinatorica 3 (1983), no. 34, 315324,
(with R.L. Graham).

On the decomposition of graphs into complete
bipartite subgraphs
Studies in Pure Mathematics Akadémiai Kiadó, Budapest, (1983) 95101,
(with P. Erdös and J. Spencer).

On a Ramseytype problem,
J. Graph Theory 7 (1983), no. 1, 7983.

On complete bipartite subgraphs contained in
spanning tree complements,
Studies in Pure Mathematics, (ed.inchief P. Erdös) Akadémiai Kiadó, Budapest, (1983)
8390,
(with B. Bollobas and R. L. Graham).

A new bound for Euclidean Steiner minimal
trees,
Discrete geometry and convexity (New York, 1982), 328346,
Ann. New York Acad. Sci. 440, New York Acad. Sci., New York, 1985,
(with R. L. Graham).

Trianglefree graphs with restricted bandwidth,
Progress in graph theory (Waterloo, Ont., 1982), 175190, Academic Press,
Toronto, ON, 1984,
(with W.T. Trotter, Jr.).

On the minimum dominating pair number of
a class of graphs,
Caribbean J. Math. 1 (1982), no. 2, 7376,
(with R.L. Graham, E.J. Cockayne, and D.J. Miller).

Minimal decompositions of hypergraphs into mutually
isomorphic subhypergraphs,
J. Comb. Th. (A) 32 (1982), 241251,
(with P. Erdös and R. L. Graham).

Tiling rectangles with rectangles,
Math. Mag. 55 (1982), no. 5, 286291,
(with E. N. Gilbert, and R. L. Graham).

On graphs which contain all sparse graphs,
Annals of Discrete Math. 12 (1982), 2126,
(with L. Babai, P. Erdös, R. L. Graham, and J. Spencer).

On packing twodimensional bins,
SIAM J. Algebraic Discrete Methods 3 (1982), no. 1, 6676,
(with M. R. Garey and D. S. Johnson).

The number of relation graphs,
Bell Laboratories Internal Memorandum, 1982,
(with F. K. Hwang and D. H. Krantz).

A note on subtrees in tournaments,
Bell Laboratories Internal Memorandum, 1982.

Minimal decomposition of all graphs
with equinumerous vertices and edges into mutually isomorphic subgraphs,
Finite and infinite sets, Vol. I, II (Eger, 1981), 171179, Colloq. Math.
Soc. János Bolyai 37, NorthHolland, Amsterdam, 1984,
(with P. Erdös and R. L. Graham).

Efficient realization techniques for network
flow patterns,
Bell System Tech. J. 60 (1981), no. 8, 17711786,
(with R. L. Graham and F. K. Hwang).

On irregularities of distribution of
real sequences,
Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 7, part 1, 4001,
longer version: On irregularities of distribution,
Finite and infinite sets, Vol. I, II (Eger, 1981), 181222, Colloq. Math. Soc. János
Bolyai, 37, NorthHolland, Amsterdam, 1984,
(with R. L. Graham).

Recent results in graph decompositions,
Combinatorics (Swansea, 1981), pp. 103123, London Math. Soc. Lecture Note Ser. 52,
Cambridge Univ. Press, CambridgeNew York, 1981,
(with R. L. Graham).

Universal caterpillars,
J. Comb. Th. (B) 31 (1981), 348355,
(with R. L. Graham and J. Shearer).

On the permanents of complements of the direct
sum of identity matrices,
Adv. in Applied Math. 2 (1981), 121137,
(with P. Diaconis, R. L. Graham, and C. L. Mallows).

Some problems and results on labelings of graphs,
The Theory and Applications of Graphs (ed. G. Chartrand), John Wiley and Sons (1981), 255264.

On the bandwidths of a graph and its complement,
The Theory and Applications of Graphs (ed. G. Chartrand), John Wiley and Sons (1981), 243253,
(with P. Z. Chinn, P. Erdös and R. L. Graham).

On trees containing all small trees,
The Theory of Applications of Graphs (ed. by G. Chartrand) John Wiley and
Sons, (1981) 265272, (with R. L. Graham and D. Coppersmith).

Minimal decomposition of graphs into mutually
isomorphic subgraphs,
Combinatorica 1 (1981), 1324,
(with P. Erdös and R. L. Graham).

A note on constructive methods for Ramsey numbers,
J. Graph Theory 5 (1981), 109113.

On Steiner trees for bounded point sets,
Geometriae Dedicata 11 (1981), 353361,
(with R. L. Graham).

On the decompositions of graphs,
SIAM J. Alg. Disc. Methods 2 (1981), 112.

Rotatable graceful graphs,
Ars Combinatoria 11 (1981), 239250,
(with F. K. Hwang).
19751980
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On unimodality for linear extensions of partial
orders,
SIAM J. Alg. Disc. Methods 1 (1980), 405410,
(with R. L. Graham and F. C. Fishburn).

The connection patterns of two complete binary
trees,
SIAM J. Alg. Disc. Methods 1 (1980), 322335,
(with F. K. Hwang).

On unimodal subsequences,
J. Comb. Th. (A) 29 (1980), 267279.

Optimal spreading in ndimensional rectilinear
grids,
Stud. Appl. Math. 62 (1980), 6774,
(with D. J. Kleitman (PECK)).

On switching networks and block designs, II,
Bell System Tech. J. 59 (1980), 11651173.

On the coverings of graphs,
Discrete Math. 30 (1980), 8993.

On universal graphs,
Annals of the New York Academy of Sciences 319 (1979), 136140,
(with R. L. Graham).

Minimal decompositions of two graphs into pairwise isomorphic subgraphs,
Proceedings of the 10th Southeastern Conf. on Comb., Graph Theory and Computing (1979), 318,
(with P. Erdos, R.L. Graham, S.M. Ulam and F.F. Yao).

Maximum antichains of rectangular arrays,
J. Comb. Theory 27 (1979), 397400,
(with R. L. Graham, P. Erdös, D. J. Kleitman, D. West, and G. Purdy (G. W. Peck)).

On concentrators, superconcentrators, generalizers,
and nonblocking networks,
Bell System Tech. J. 58 (1979), 17651777.

On the product of the point and line covering
numbers of a graph,
Annals of the New York Academy of Sciences 319 (1979), 597602,
(with P. Erdös and R. L. Graham).

The largest minimal rectilinear Steiner trees
for a set of n points enclosed in a rectangle with given perimeter,
Networks 9 (1979), 1936,
(with F. K. Hwang).

A conjectured minimum valuation tree,
Problems and solutions, SIAM Review 20 (1978), 601604.

Zonebalanced networks and block designs,
Bell System Tech. J. 57 (1978), 29572971.

The number of Baxter permutations,
J. Comb. Th. (A) 24 (1978), 382394,
(with R. L. Graham, V. E. Hoggatt, and M. Kleiman).

Optimal multistage switching networks,
IEEE Trans. on Communications COM26 (1978), 12821287.

On blocking probabilities for a class of linear
graphs,
Bell Systems Tech. J. 57 (1978), 29152925,
(with F. K. Hwang).

A generalization of Takagi's Theorem on
optimal channel graphs,
Bell System Tech. J. 57 (1978), 171178,
(with F. K. Hwang).

On partitions of graphs into trees,
Discrete Math. 23 (1978), 2330.

An algebraic approach to switching networks,
Bell Laboratories Internal Memorandom, 1978.

Steiner trees for ladders,
Annals of Discrete Math. 2 (1978), 173200,
(with R. L. Graham).

Do stronger players win more knockout tournaments?,
JASA 73 (1978), 593596,
(with F. K. Hwang).

A lower bound for the Steiner tree problem,
SIAM J. on Applied Math. (B) 34 (1978), 2736,
(with F. K. Hwang).

On graphs which contain all small trees,
J. Comb. Th. (B) 24 (1978), 1423,
(with R. L. Graham).

A problem on blocking probabilities in connecting
networks,
Networks 7 (1977), 185192,
(with F. K. Hwang). 
On blocking probabilities for switching networks,
Bell System Tech. J. 56 (1977), 14311446,
(with F. K. Hwang).

Some results on hook lengths,
Discrete Math. 20 (1977), 3340,
(with J. E. Herman).

On switching networks and block designs,
Conf. Record of the 10th Asilomar conf. on Circuits System and Computers
(1976), 212218.

On the set of distances determined by the union of
arithmetic progressions,
Ars Combinatoria 1 (1976), 5776,
(with R. L. Graham).

On graphs which contain all small trees II,
Colloquia Mathematica Societatis János Bolyai, Keszthely, Hungary, (1976), 213223,
(with R. L. Graham and N. Pippenger).

Steiner trees for the regular simplex,
Bull. of the Inst. of Math., Academia Sinica, 4 (1976), 313325,
(with E. N. Gilbert).
19731975
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On multicolor Ramsey numbers for complete bipartite
graphs,
J. Comb. Th. (B) 18 (1975), 164169,
(with R. L. Graham).

Optimal Rearrangeable graphs,
Bell System Tech. J. 54 (1975), 16471661.

On triangular and cyclic Ramsey numbers with
k colors,
Graphs and Combinatorics, Lecture Notes, No. 406, (1974), 236242, SpringerVerlag, New York.

On the Ramsey numbers N(3,3,...,3;2),
Discrete Math. 5 (1973), 317321.
