Classes of graphs with small rank decompositions are chi-bounded

2011/07/11 by Dvorak, Zdenek, Kral, Daniel
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1107.2161

Abstract

A class of graphs G is chi-bounded if the chromatic number of graphs in G is bounded by a function of the clique number. We show that if a class G is chi-bounded,then every class of graphs admitting a decomposition along cuts of small rank to graphs from G is chi-bounded. As a corollary, we obtain that every class of graphs with bounded rank-width (or equivalently, clique-width) is chi-bounded.

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