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Colouring diamond-free graphs.

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

Abstract

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.

Item Type:Book chapter
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Available under License - Creative Commons Attribution.
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.4230/LIPIcs.SWAT.2016.16
Publisher statement:© Konrad K. Dabrowski, François Dross, and Daniël Paulusma; licensed under Creative Commons License CC-BY
Date accepted:01 April 2016
Date deposited:01 July 2016
Date of first online publication:June 2016
Date first made open access:No date available

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