The game chromatic number of random graphs
Combinatorics
2007-07-04 v1
Abstract
Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are colored. The game chromatic number \chi_g(G) is the minimum k for which the first player has a winning strategy. In this paper we analyze the asymptotic behavior of this parameter for a random graph G_{n,p}. We show that with high probability the game chromatic number of G_{n,p} is at least twice its chromatic number but, up to a multiplicative constant, has the same order of magnitude. We also study the game chromatic number of random bipartite graphs.
Keywords
Cite
@article{arxiv.0707.0465,
title = {The game chromatic number of random graphs},
author = {Tom Bohman and Alan Frieze and Benny Sudakov},
journal= {arXiv preprint arXiv:0707.0465},
year = {2007}
}