Classes of graphs with small rank decompositions are χ-bounded

• DOI: 10.1016/j.ejc.2011.12.005
• Publication Date: 2012-01-18T15:29:50Z
• Authors: Zdeněk Dvořák; Daniel Král’
• Keywords: Rank (graph theory)

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.