Classes of graphs with small rank decompositions are chi-bounded

Details Classes of graphs with small rank decompositions are chi-bounded Classes of graphs with small rank decompositions are chi-bounded

2011-07-11

arxiv.org/abs/1107.2161v1

Mathematics

Combinatorics

Scientific paper

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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