8 years 6 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»
8 years 9 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»
8 years 9 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
8 years 10 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»
8 years 11 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»
8 years 11 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»
8 years 11 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»
8 years 11 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»
8 years 11 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»
8 years 11 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