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Durham University

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Publication details

Dabrowski, K.K., Dross, F. & Paulusma, D. (2016), Colouring diamond-free graphs, in Pagh, Rasmus eds, Leibniz International Proceedings in Informatics (LIPIcs) 53: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Reykjavik, Iceland, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Wadern, 16.

Author(s) from Durham


The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we classify the computational complexity of Colouring for (diamond,H)-free graphs. Our proof is based on combining known results together with proving that the clique-width is bounded for (diamond,P_1+2P_2)-free graphs. Our technique for handling this case is to reduce the graph under consideration to a k-partite graph that has a very specific decomposition. As a by-product of this general technique we are also able to prove boundedness of clique-width for four other new classes of (H_1,H_2)-free graphs. As such, our work also continues a recent systematic study into the (un)boundedness of clique-width of (H_1,H_2)-free graphs, and our five new classes of bounded clique-width reduce the number of open cases from 13 to 8.


Conference date: 22-24 June 2016