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Durham University

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Dabrowski, K.K., Huang, S. & Paulusma, D. (2015), Bounding clique-width via perfect graphs, in Dediu, Adrian-Horia, Formenti, Enrico, Martín-Vide, Carlos & Truthe, Bianca eds, Lecture Notes in Computer Science 8977: International Conference on Language and Automata Theory and Applications. Nice, France, Springer, Nice, 676-688.

Author(s) from Durham


Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1,H2)-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 (H1,H2)-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 clique-width we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.