The game chromatic number of random graphs

: 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 g(G) is the minimum k for which the first player has a winning strategy. In this study, we analyze the asymptotic behavior of this parameter for a random graph Gn,p. We show that with high probability, the game chromatic number of Gn,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.

• Type: Journal
• Year: 2008
• Where: RSA
• Authors: Tom Bohman, Alan M. Frieze, Benny Sudakov
• Keywords: Asymptotic Behavior, Game Chromatic Number, RSA 2008, Winning Strategy