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2008

The game chromatic number of random graphs

8 years 10 months ago
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.
Tom Bohman, Alan M. Frieze, Benny Sudakov
Added 28 Dec 2010
Updated 28 Dec 2010
Type Journal
Year 2008
Where RSA
Authors Tom Bohman, Alan M. Frieze, Benny Sudakov
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