Bounding clique-width via perfect graphs

Abstract

Given two graphs H 1 and H 2, a graph G is (H 1,H 2)-free if it contains no subgraph isomorphic to H 1 or H 2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H 1,H 2)-free graphs that have bounded clique-width. We also show the implications of our results for the computational complexity of the Colouring problem restricted to (H 1,H 2)-free graphs. The three new graph classes have in common that one of their two forbidden induced subgraphs is the diamond (the graph obtained from a clique on four vertices by deleting one edge). To prove boundedness of their cliquewidth we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.