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arXiv · 0707.0465

The game chromatic number of random graphs

Tom Bohman·Alan Frieze·Benny Sudakov
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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 χ_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.

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Tom Bohman, Alan Frieze, Benny Sudakov. 2007-07-03. The game chromatic number of random graphs. https://arxiv.org/abs/0707.0465

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