Publication detailsDabrowski, K.K., Dross, F. & Paulusma, D. (2017). Colouring Diamond-free Graphs. Journal of Computer and System Sciences 89: 410-431.
- Publication type: Journal Article
- ISSN/ISBN: 0022-0000
- DOI: 10.1016/j.jcss.2017.06.005
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
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,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.