Colouring Diamond-free Graphs

Dabrowski, K.K.; Dross, F.; Paulusma, D.

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,P1+2P2)-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 (H1,H2)-free graphs. As such, our work also continues a recent systematic study into the (un)boundedness of clique-width of (H1,H2)-free graphs, and our five new classes of bounded clique-width reduce the number of open cases from 13 to 8.

Citation

Dabrowski, K., Dross, F., & Paulusma, D. (2017). Colouring Diamond-free Graphs. Journal of Computer and System Sciences, 89, 410-431. https://doi.org/10.1016/j.jcss.2017.06.005

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2017
• Online Publication Date: Jun 22, 2017
• Publication Date: Nov 1, 2017
• Deposit Date: Jun 12, 2017
• Publicly Available Date: Jun 13, 2017
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Electronic ISSN: 1090-2724
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 89
• Pages: 410-431
• DOI: https://doi.org/10.1016/j.jcss.2017.06.005
• Public URL: https://durham-repository.worktribe.com/output/1385307