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The game chromatic number of random graphs
Author(s) -
Bohman Tom,
Frieze Alan,
Sudakov Benny
Publication year - 2008
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20179
Subject(s) - combinatorics , bipartite graph , mathematics , chromatic scale , multiplicative function , random graph , discrete mathematics , graph , brooks' theorem , edge coloring , graph power , line graph , mathematical analysis
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 study, 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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008
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