ROUTING PERMUTATIONS ON GRAPHS VIA MATCHINGS* (2009)
Abstract. A class of routing problems on connected graphs G is considered. Initially, each vertex v of G is occupied by a "pebble " that has a unique destination (v) in G (so that r...
ADVANCES IN APPLIED MATHEMATICS 4, 175- 196 ( 1983) The Mathematics of Perfect Shuffles (2008)
Persi Diaconis, R. L. Graham, William M. Kantor
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves...
R. L. Graham, H. S. Witsenhausen, H. J. Zassenhaus
obtaining a packing inequality for finite plane simplicial complexes that are admissible for Euclidean distance is generalized for arbitrary Minkowski distances, a slackness measure is defined and...
Ronald L. Graham, Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan, R. L. Graham
Abstract. This paper gives n-dimensional analogues of the Apollonian circle packings in Parts I and II. Those papers considered circle packings described in terms of their Descartes configurations,...
ON THE FRACTIONAL COVERING NUMBER OF HYPERGRAPHS* (2008)
Abstract. Thefractional covering number r * ofa hypergraphH (V, E) is defined to be the minimum possible value of,,v t(x) where ranges over all functions t: V which satisfy,xe t(x)> = for all...
Geometry © 1998 Springer-Verlag New York Inc. Forced Convex n-Gons in the Plane ∗ (2008)
R. L. Graham, Communicated János Pach, R. L. Graham
Abstract. In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g(n) such that any subset of g(n) points in the plane in general position must always...
B. D. Lubachevsky, R. L. Graham
Abstract. For each k ≥ 1 and corresponding hexagonal number h(k) = 3k(k + 1) + 1, we introduce m(k) = max{(k − 1)!/2, 1} packings of h(k) equal disks inside a circle which we call the curved...
Ronald L. Graham, Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan, R. L. Graham
Abstract. Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings...
Ronald L. Graham, Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan, R. L. Graham
Abstract. Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the...
ON FINITE SUMS OF RECIPROCALS OF DISTINCT nTR POWERS (2008)
Introduction * It has long been known that every positive rational number can be represented as a finite sum of reciprocals of distinct positive integers (the first proof having been given by...
Abstract Infiniband Scalability in Open MPI (2008)
G. M. Shipman, T. S. Woodall, R. L. Graham, A. B. Maccabe
Inifiniband is becoming an important interconnect technology in high performance computing. Recent efforts in large scale Infiniband deployments are raising scalability questions in the HPC...
Innovative Computing Laboratory, (2008)
B. Barrett, J. M. Squyres, A. Lumsdaine, R. L. Graham, G. Bosilca
Abstract. Component architectures provide a useful framework for developing an extensible and maintainable code base upon which largescale software projects can be built. Component methodologies have...
Routing permutations on graphs via matchings (extended abstract) Abstract (2008)
We consider a class of routing problems on con-nected graphs G. Initially, each vertex v of G is occupied by a “pebble ” which has a unique desti-nation T(V) in G, so that m is a permutation of...
Ramsey Theory in the Work of Paul Erd}os (2008)
Summary. Ramsey's theorem was not discovered by P. Erd}os. But perhaps one could say that Ramsey theory was created largely by him. This paper will attempt to demonstrate this claim. 1.
ADVANCES IN APPLIED MATHEMATICS 4, 175- 196 ( 1983) The Mathematics of Perfect Shuffles (2008)
Persi Diaconis, R. L. Graham, William M. Kantor
There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves...
S. Dulucq, O. Guibert, R. L. Graham, V. E. Hoggatt, ...
F.R.K. Chung, R.L. Graham, V.E. Hoggatt and M. Kleiman [2] have shown the number of Baxter's permutations on [n] is P n\Gamma1 m=0 ( n+1 m ):( n+1 m+1 ):( n+1 m+2 ) ( n+1 1 ) : ( n+1 2 ) . X....
Geometry © 1998 Springer-Verlag New York Inc. Forced Convex n-Gons in the Plane ∗ (2007)
Communicated János Pach, R. L. Graham, R. L. Graham
Abstract. In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g(n) such that any subset of g(n) points in the plane in general position must always...
We provide an elementary proof of the fact that the ramsey number of every bipartite graph H with maximum degree at most is less than 8(8) jV (H)j. This improves an old upper bound on the ramsey...
Analysis of the component architecture overhead (2005)
B. Barrett, J. M. Squyres, A. Lumsdaine, R. L. Graham, G. Bosilca
Abstract. Component architectures provide a useful framework for developing an extensible and maintainable code base upon which largescale software projects can be built. Component methodologies have...
Curved Hexagonal Packings of Equal Disks in a Circle (2004)
Lubachevsky, B. D., Graham, R. L.
For each k >= 1 and corresponding hexagonal number h(k) = 3k(k+1)+1, we introduce m(k) = max[(k-1)!/ 2, 1] packings of h(k) equal disks inside a circle which we call "the curved hexagonal packings"....
TEG: A high-performance, scalable, multi-network point-to-point communications methodology (2004)
T. S. Woodall, R. L. Graham, R. H. Castain, D. J. Daniel, M. W. Sukalski, E. Gabriel, ...
Abstract. TEG is a new component-based methodology for point-to-point messaging. Developed as part of the Open MPI project, TEG provides a configurable fault-tolerant capability for high-performance...
TEG: A high-performance, scalable, multi-network point-to-point communications methodology (2004)
T. S. Woodall, R. L. Graham, R. H. Castain, D. J. Daniel, M. W. Sukalski, G. E. Fagg, ...
Abstract. TEG is a new component-based methodology for point-to-point messaging. Developed as part of the Open MPI project, TEG provides a configurable fault-tolerant capability for high-performance...
T. S. Woodall, R. L. Graham, R. H. Castain, D. J. Daniel, M. W. Sukalski, G. E. Fagg, ...
Abstract. TEG is a new methodology for point-to-point messaging developed as a part of the Open MPI project. Initial performance measurements are presented, showing comparable ping-pong latencies in...
T. S. Woodall, R. L. Graham, R. H. Castain, D. J. Daniel, M. W. Sukalski, G. E. Fagg, ...
Abstract. TEG is a new methodology for point-to-point messaging developed as a part of the Open MPI project. Initial performance measurements are presented, showing comparable ping-pong latencies in...
On Packing Squares with Equal Squares, (2002)
The following problem arises in connection with certain multidimensional stock cutting problems: How many non-overlapping open unit squares may be packed into a large square of side alpha. Of course,...
Distance Matrices of Trees. (2002)
Prepared in cooperation with Bell Labs., Murray Hill, N.J., and Eotvos Lorand Univ., Budapest (Hungary).
Addition Chains with Multiplicative Cost, (2002)
Graham,R. L., Yao,A. C-C., Yao,F-F.
If each step in an addition chain is assigned a cost equal to the product of the numbers added at that step, 'binary' addition chains are shown to minimize total cost.
Spearman's Footrule as a Measure of Disarray. (2002)
Spearman's rho and Kendall tau are related to two less widely used measures of association: Spearman's footrule and the minimum number of transitions. The means, variances, and limiting normality of...
On Constant Weight Codes and Harmonious Graphs. (2002)
Very recently a new method has been developed for finding lower bounds on the maximum number of codewords possible in a code of minimum distance d and length n. This method has led in turn to a...
On Graphs with Linear Ramsey Numbers (2001)
R. L. Graham, V. Rödl, A. Rucinski, A. Mickiewicz
For a fixed graph H, the ramsey number r(H) is defined to be the least integer N such that in any 2-coloring of the edges of the complete graph KN , some monochromatic copy of H is always formed. Let...
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions (2000)
Graham, R. L., Lagarias, J. C., Mallows, C. L., Wilks, A. R., Yan, C. H.
This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all $n$-dimensional oriented Descartes configurations...
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group (2000)
Graham, R. L., Lagarias, J. C., Mallows, C. L., Wilks, A. R., Yan, C. H.
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have...
Graham, R. L., Lagarias, J. C., Mallows, C. L., Wilks, A. R., Yan, C. H.
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes...
Apollonian Circle Packings: Number Theory (2000)
Graham, R. L., Lagarias, J. C., Mallows, C. L., Wilks, A. R., Yan, C. H.
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer...
On graphs with linear Ramsey numbers (2000)
R. L. Graham, V. Roè Dl, A. Rucinâ Ski
Abstract: For a ®xed graph H, the Ramsey number r (H) is de®ned to be the least integer N such that in any 2-coloring of the edges of the complete graph KN, some monochromatic copy of H is always...
R. L. Graham, V. R Ödl, A. Ruci Ński
We provide an elementary proof of the fact that the ramsey number of every bipartite graph H withmaximum degree at most ∆ is less than 8(8∆) ∆ |V (H)|. This improves an old upper bound on the...
ADAPTATION OF WRENSS-FORTRAN-77 FOR A GIS APPLICATION FOR WATER-YIELD CHANGES (1999)
D. D. Huff, W. W. Hargrove, R. L. Graham
Managed by
Graham,R. L., Murray,G., Geiger,J. S.
Momentum ratios of some of the more intense internal conversion lines from sources of thorium radioactive deposit have been determined with accuracies of 1 to 4 parts in 100,000 using an iron-free...
Herrlander,C. J., Graham,R. L.
Conversion lines of the 279.16=0.02 and 401.27=0.05 keV transitions in T1203 have been studied at high resolution (=0.07% in momentum). From the measured line intensities and the known total...
On Sparse Graphs with Dense Long Paths. (1998)
Erdos,P., Graham,R. L., Szemeredi,E.
The following problem was raised by H.-J. Stoss in connection with certain questions related to the complexity of Boolean functions. An acyclic directed graph G is said to have property p (m,n) if...
ACARP - Australian Coal Associaiton Research Program - research that makes a difference (1998)
Coal exports are forecast to grow strongly, so that coal is likely to remain very important to Australia for the foreseeable future. However there is no sign that prices or profitability will rise of...
ACARP - Australian Coal Associaiton Research Program - research that makes a difference (1998)
Coal exports are forecast to grow strongly, so that coal is likely to remain very important to Australia for the foreseeable future. However there is no sign that prices or profitability will rise of...
ACARP - Australian Coal Associaiton Research Program - research that makes a difference (1998)
Coal exports are forecast to grow strongly, so that coal is likely to remain very important to Australia for the foreseeable future. However there is no sign that prices or profitability will rise of...
Random walks on generating sets for finite groups (1997)
Dedicated to Herb Wilf on the occasion of his sixty-fifth birthday We analyze a certain random walk on the cartesian product G n of a finite group G which is often used for generating random elements...
Random walks on generating sets for finite groups (1997)
Dedicated to Herb Wilf on the occasion of his sixty-fifth birthday We analyze a certain random walk on the cartesian product G n of a finite group G which is often used for generating random elements...
Random walks on generating sets for finite groups (1997)
Dedicated to Herb Wilf on the occasion of his sixty-fifth birthday We analyze a certain random walk on the cartesian product G n of a finite group G which is often used for generating random elements...
Random Walks on Generating Sets for Finite Groups (1997)
We analyze a certain random walk on the cartesian product G n of a finite group G which is often used for generating random elements from G. In particular, we show that the mixing time of the walk is...
Stratified Random Walks on the (1997)
In this paper we present a method for analyzing a general class of ramdom walks on the n-cube (and certain subgraphs of it). These walks all have the property that the transition probabilities depend...
Random Walks on Generating Sets for Finite Groups (1997)
We analyze a certain random walk on the cartesian product G n of a finite group G which is often used for generating random elements from G. In particular, we show that the mixing time of the walk is...
Stratified random walk on the n-cube (1997)
ABSTRACT: In this paper we present a method for analyzing a general class of random walks on the n-cube Ž and certain subgraphs of it.. These walks all have the property that the transition...
Forced convex n-gons in the plane (1997)
In a seminal paper from 1935, Erd}os and Szekeres showed that for each n there exists a least value g(n) such that any subset of g(n) points in the plane in general position must always contain the...
RepeatedPatternsofDensePackings of Equal Disks in a Square (1996)
R. L. Graham, B. D. Lubachevsky
We examine sequences of dense packings of n congruent non-overlapping disks inside a square which follow specific patterns as n increases along certain values, n = n(1),n(2),...n(k),.... Extending...
Low-Dimensional Lattices VII: Coordination Sequences (1996)
J.H. Conway, A. F. Wells, Three-dimensional Nets, R. L. Graham, D. E. Knuth, O. Patashnik, ...
Introduction to Combinatorial Analysis, Wiley, NY, 1958. [23] N. J. A. Sloane, Theta-series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys., 28 (1987), 1653--1657....
Stratified Random Walks on the N-Cube (1996)
this paper we present a method for analyzing a general class of random walks on the n-cube. These walks have the property that the transition probabilities (only) depend on the level (or weight) of...
Dense packings of equal disks in an equilateral triangle: from 22 to 34 and beyond (1995)
R. L. Graham, B. D. Lubachevsky
Previously published packings of equal disks in an equilateral triangle have dealt with up to 21 disks. We use a new discrete-event simulation algorithm to produce packings for up to 34 disks. For...
Dense Packings of Equal Disks in an Equilateral Triangle: From 22 to 34 and Beyond (1995)
R. L. Graham, B. D. Lubachevsky
Previously published packings of equal disks in an equilateral triangle have dealt with up to 21 disks. We use a new discrete-event simulation algorithm to produce packings for up to 34 disks. For...
Dense packings of equal disks in an equilateral triangle: from 22 to 34 and beyond (1995)
R. L. Graham, B. D. Lubachevsky
Previously published packings of equal disks in an equilateral triangle have dealt with up to 21 disks. We use a new discrete-event simulation algorithm to produce packings for up to 34 disks. For...
Routing Permutations on Graphs via Matchings (1994)
We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble ” which has a unique destination π(v) in G (so that π is a permutation of...
Communicated by the Managing Editors (1990)
It has been discovered in the past few years that there is a surprisingly large class Z? of graph properties, all shared by random graphs, which are equivalent in the following sense: If a family of...
Communicated by the Managing Editors (1990)
It has been discovered in the past few years that there is a surprisingly large class Z? of graph properties, all shared by random graphs, which are equivalent in the following sense: If a family of...
Communicated by the Managing Editors (1990)
Given positive integers d and n, there is an integer N such that for every injective map ffrom { 1..... N} a into R there is a subset A = A1 x A2 x... × Ad of { 1..... N} a such that (1) each Aj has...
Chung, F. R. K., Graham, R. L., Wilson, R. M.
We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular...
Communicated, by the Managing Editors (1988)
There are many Ramsey-type results in combinatorics for which stronger density versions actually hold. An excellent example of this phenomenon is given by the classical theorem of van der Waerden on...
Note On Induced Subgraphs of the Cube (1987)
Consider the usual graph Q ” defined by the n-dimensional cube (having 2 ” ver-tices and n2”- ’ edges). We prove that if G is an induced subgraph of Q ” with more than 2 ”- ’ vertices...
Communicated by the Managing Editors (1986)
An important topic in Ramsey theory deals with solution sets of (systems of) homogeneous linear equations. Pioneered by the early work of Schur [I91 and van der Waerden [21], the subject received a...
The induced restricted versions of the vector space Ramsey theorem and of the Graham-Rothschild parameter set theorem are proved. 1 ’ 19X7 Academtc Press. IIIC
Author: TABLE OF CONTENTS (1986)
J. Bentley, E. Coffman, R. L. Graham, D. Kuck, Luc Devroye, Luc Devroye
A short proof of the following result of Brown and Buhler is given: For any E> 0 there exists n, = no(E) such that if A is an abelian group of odd order IAl> no and BG A with IBI>&IAI....
Note The Radon Transform on Abelian Groups (1986)
The Radon transform on a group A is a linear operator on the space of functions /: A-+ C. It is shown that if A = Z;: then the Radon transform with respect to a sub-set B c.4 is not invertible if and...
The Chalk-River neutrino-mass experiment: a progress report (1985)
Graham, R.L., Lone, M.A., Andrews, H.R., Gallant, J.L., Geiger, J.S., Lee-Whiting, G.E., ...
The Chalk-River neutrino-mass experiment: a progress report (1985)
Graham, R.L., Lone, M.A., Andrews, H.R., Gallant, J.L., Geiger, J.S., Lee-Whiting, G.E., ...
An experiment to measure the electron anti-neutrino mass from the beta decay of $^3$H (1984)
Graham, R.L., Lone, M.A., Andrews, H.R., Gallant, J.L., Geiger, J.S., Lee Whiting, G.E., ...
An experiment to measure the electron anti-neutrino mass from the beta decay of $^3$H (1984)
Graham, R.L., Lone, M.A., Andrews, H.R., Gallant, J.L., Geiger, J.S., Lee Whiting, G.E., ...
An anti-Hadamard matrix may be loosely defined as a real (0,1) matrix which is invertible, but only just. Let A be an invertible (0,1) matrix with eigenvalues l i , singular values s i , and inverse...
An anti-Hadamard matrix may be loosely defined as a real (0,1) matrix which is invertible, but only just. Let A be an invertible (0,1) matrix with eigenvalues λ i, singular values σ i, and inverse...
R. L. Graham, P. Frankl, J. B. Shearer
A classical topic in combinatorics is the study of problems of the following type: What are the maximum families F of subsets of a finite set with the property that the intersection of any two sets...
A classic theorem of van der Waerden asserts that for any positive integer k, there is an integer W(k) with the property that if IV> W(k) and the set { 1,2,..., W} is partitioned into r classes...
On universal graphs for spanning trees (1983)
A number of papers [1,2,3,4,6] recently have been concerned with the following question. What is the minimum number s{n) of edges a graph G on n vertices can have so that any tree on n vertices is...
Communicated by the Managing Editors (1983)
In an influential paper published in 1892, Hilbert proved the following result, which in some sense could be considered the first theorem in Ram-sey theory. For positive integers m, a, and ak, 1 Q k...
The probletn of determining a phylogeny of maximum parsimony from a Fjiven set of protein sequences is defined. It is shown that this problem is what is called, i 1 computer science, NP-complete. The...
W. Deuber, R. L. Graham, H. J. Promel, B. Voigt
A canonical version of the multidimensional version of van der Waerden’s theorem on arithmetic progressions is proved. 1.
THE OCCASION OF HIS RETIREMENT (1981)
By an r-uniform hypergraph (or r-graph, for short) H = (V, E) we mean a collection E = E(H) = {E I E m} of r-element subsets (called edges) of a set V = V(H), called the vertices of H. Let K = {H...
On the permanents of complements of the direct sums of identity matrices, Adv (1981)
A classic experiment used in testing for ESP abilities has the following general form. A deck of cards, consisting of a, identical cards of type i, 1 I i I r, is shuffled and placed face down (in...
Communicated by the Editors (1981)
For a class V of graphs, denote by a(@?) the least value of m so that for some graph II on m vertices, every GE Q occurs as a subgraph of U. In this note we obtain rather sharp bounds on u(q) when Q...
THE OCCASION OF HIS RETIREMENT (1981)
By an r-uniform hypergraph (or r-graph, for short) H = (V, E) we mean a collection E = E(H) = {E,,..., E,] of r-element subsets (called edges) of a set V = V(H), called the vertices of H. Let 3’ =...
Communicated by the Editors (1981)
For a class V of graphs, denote by a(@?) the least value of m so that for some graph II on m vertices, every GE Q occurs as a subgraph of U. In this note we obtain rather sharp bounds on u(q) when Q...
On the structure of t-designs (1980)
Abstract. It is possible toviewthecombinatorial structuresknown as (integral) t-designs asZ-modules in a natural way. In this note we introduce a polynomial associated to each such Z-module. Using...
For fixed positive integers n and r, let x be a mapping of the integer points Z” = {(z,,..., z,): zk an integer) into { l,..., r}. Denote by L(x) the maximum number of consecutive collinear points...
Suppose 9. =!{pGl,..., Gk} is a collection of graphs, all having n vertices and e edges. By a U-decomposition of T „ we mean a set of partitions of the edge sets E(G,) of the G,, say E(G,)= = E...
JOURNAL OF COMBINATORIAL THEORY, Series A 28, 89-91 (1980) On Partitions of [En (1978)
Euclidean Ramsey theory [i-3] is that branch of combinatorics which deals with questions of the following type: Which finite subsets C of lE ” have the property that for any partition of Euclidean...
Distance matrix polynomials of trees (1978)
Let G be a finite connected graph. If x and y are vertices of G, one may define a distance function d, on G by letting d&x, y) be the minimal length of any path between x and y in G (with d&,...
DEDICATED TO JOHN RIORDAN ON THE OCCASION OF HIS 75TH BIRTHDAY BACKGROUND (1977)
R. L. Graham, V. E. Hoggatt, M. Kleiman
permutations apparently first arose in attempts to prove the “commuting function ” conjecture of Dyer (see [I]), namely, if f and g are continuous functions mapping [0, l] into [0, l] which...
Communicated by the Managing Editors (1975)
For finite graphs F and G, let Nr(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. If g and c?? are families of graphs, it is natural to...
JOURNAL OF COMJSINATORIAL THEORY @) 18, 86 % (1975) On Cubical Graphs (1974)
It is frequently of interest to represent a given graph G as a subgraph of a graph H which has some special structure. A particularly useful class of graphs in which to embed G is the class of...
Performance bounds on the splitting algorithm for binary testing (1974)
Summary. In machine fault-location, medical diagnosis, species identification, and computer decisionmaking, one is often required to identify some unknown object or condition, belonging to a known...
Stanford University and The Hungarian Academy of Sciences (1974)
The following problem arises in connection with certain multidimensional stock cutting problems: How many nonoverlapping open unit squares may be packed into a large square of side a? Of course, if a...
JOURNAL OF COMBINATORIAL THEORY (A) 18, 165470 (1975) The Largest Small Hexagon (1974)
The problem of determining the largest area a plane hexagon of unit diameter can have, raised some 20 years ago by H. Lenz, is settled. It is shown that such a hexagon is unique and has an area...
R. L. Graham, P. Montgomery, B. L. Rothschild, J. Spencer
DEDICATED TO THE MEMORY OF THEODORE S. MOTZKIN The general Ramsey problem can be described as follows: Let A and B be two sets, and R a subset of A x B. For a E A denote by R(a) the set {b E B I (a,...
Bounds on Multiprocessing Timing Anomalies (1969)
SIAM Journal on Applied Mathematics is currently published by Society for Industrial and Applied Mathematics.
Irregularities in the Distributions of Finite Sequences (1968)
E. R. Berlekamp, R. L. Graham, Communicated H. Mann
Suppose (x1, x1,..., xs+J is a sequence of numbers with xi E [0, 1) which has the property that for each r < s and for each k < r, the subinterval [k/r, (k + l/n)) contains at least one point...
Chung, F. R. K., Graham, R. L., Wilson, R. M.
We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular...
Chung, F. R. K., Graham, R. L.
We describe a large equivalence class of properties shared by most hypergraphs, including so-called random hypergraphs. As a result, it follows that many global properties of hypergraphs are actually...
On irregularities of distribution of real sequences
Chung, F. R. K., Graham, R. L.
A natural measure of the amount of unavoidable clustering that must occur in any bounded infinite sequence of real numbers is studied. We determine the extreme value for this measure and exhibit...
Isometric embeddings of graphs
We prove that any finite undirected graph can be canonically embedded isometrically into a maximum cartesian product of irreducible factors.
Ramsey's Theorem for a Class of Categories
Graham, R. L., Leeb, K., Rothschild, B. L.
Ramsey's Theorem states that for a sufficiently large set S, and for any splitting of the k-element subsets of S into r classes, there is a subset T [unk] S, [unk]T[unk] = l, such that all k-element...
Chung, F. R. K., Graham, R. L., Wilson, R. M.
We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular...
Chung, F. R. K., Graham, R. L.
We describe a large equivalence class of properties shared by most hypergraphs, including so-called random hypergraphs. As a result, it follows that many global properties of hypergraphs are actually...
On irregularities of distribution of real sequences
Chung, F. R. K., Graham, R. L.
A natural measure of the amount of unavoidable clustering that must occur in any bounded infinite sequence of real numbers is studied. We determine the extreme value for this measure and exhibit...
Isometric embeddings of graphs
We prove that any finite undirected graph can be canonically embedded isometrically into a maximum cartesian product of irreducible factors.
Ramsey's Theorem for a Class of Categories
Graham, R. L., Leeb, K., Rothschild, B. L.
Ramsey's Theorem states that for a sufficiently large set S, and for any splitting of the k-element subsets of S into r classes, there is a subset T [unk] S, [unk]T[unk] = l, such that all k-element...