We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Colouring of graphs with Ramsey-type forbidden subgraphs.

Dabrowski, K.K. and Golovach, P.A. and Paulusma, D. (2013) 'Colouring of graphs with Ramsey-type forbidden subgraphs.', in Graph-theoretic concepts in computer science : 39th International Workshop, WG 2013, 19-21 June 2013, Lübeck, Germany ; revised papers. Berlin, Heidelberg: Springer, pp. 201-212. Lecture notes in computer science. (8165).


A colouring of a graph G = (V;E) is a mapping c : V ! f1; 2; : : :g such that c(u) 6= c(v) if uv 2 E; if jc(V )j k then c is a k-colouring. The Colouring problem is that of testing whether a given graph has a k-colouring for some given integer k. If a graph contains no induced subgraph isomorphic to any graph in some family H, then it is called H-free. The complexity of Colouring for H-free graphs with jHj = 1 has been completely classied. When jHj = 2, the classication is still wide open, although many partial results are known. We continue this line of research and forbid induced subgraphs fH1;H2g, where we allow H1 to have a single edge and H2 to have a single nonedge. Instead of showing only polynomial-time solvability, we prove that Colouring on such graphs is xed-parameter tractable when parameterized by jH1j + jH2j. As a byproduct, we obtain the same result both for the problem of determining a maximum independent set and for the problem of determining a maximum clique.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:14 January 2015
Date of first online publication:2013
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar