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10 years 8 months ago
The period of the Bell numbers modulo a prime
We discuss the numbers in the title, and in particular whether the minimum period of the Bell numbers modulo a prime p can be a proper divisor of Np = (pp - 1)/(p - 1). It is known...
Peter L. Montgomery, Sangil Nahm, Samuel S. Wagsta...
105views more  DAM 2010»
10 years 11 months ago
An iterative approach to graph irregularity strength
An assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength,...
Michael Ferrara, Ronald J. Gould, Michal Karonski,...
74views more  CPC 2010»
10 years 11 months ago
Playing to Retain the Advantage
Let P be a monotone increasing graph property, let G = (V, E) be a graph, and let q be a positive integer. In this paper, we study the (1 : q) Maker-Breaker game, played on the ed...
Noga Alon, Dan Hefetz, Michael Krivelevich
10 years 11 months ago
The effect of girth on the kernelization complexity of Connected Dominating Set
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
Neeldhara Misra, Geevarghese Philip, Venkatesh Ram...
95views more  IPL 1998»
11 years 1 months ago
Coloring Random Graphs
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exis...
Michael Krivelevich, Benny Sudakov
82views more  COMBINATORICS 1999»
11 years 1 months ago
2-adic Behavior of Numbers of Domino Tilings
We study the 2-adic behavior of the number of domino tilings of a 2n
Henry Cohn
107views more  ENDM 2002»
11 years 1 months ago
Edge-Colorings of Complete Graphs that Avoid Polychromatic Trees
Given a positive integer n and a family F of graphs, let R(n, F) denote the maximum number of colors in an edge-coloring of Kn such that no subgraph of Kn belonging to F has disti...
Tao Jiang, Douglas B. West
74views more  ENDM 2002»
11 years 1 months ago
Vertex Coverings by Coloured Induced Graphs - Frames and Umbrellas
A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex y of H there is an induced copy of G in H with x at y. The graph G uniformly embeds in H if...
Wayne Goddard, Michael A. Henning
93views more  DM 2002»
11 years 1 months ago
New constructions of non-adaptive and error-tolerance pooling designs
We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be
Hung Q. Ngo, Ding-Zhu Du
90views more  DAM 2002»
11 years 1 months ago
k-Subdomination in graphs
For a positive integer k, a k-subdominating function of a graph G = (V; E) is a function f : V {-1; 1} such that uNG[v] f(u)
Gerard J. Chang, Sheng-Chyang Liaw, Hong-Gwa Yeh