K. K. Dabrowski
Colouring of Graphs with Ramsey-Type Forbidden Subgraphs
Dabrowski, K. K.; Golovach, P. A.; Paulusma, D.
Authors
Contributors
Andreas Brandstädt
Editor
Klaus Jansen
Editor
Rüdiger Reischuk
Editor
Abstract
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.
Citation
Dabrowski, K. K., Golovach, P. A., & Paulusma, D. (2013). Colouring of Graphs with Ramsey-Type Forbidden Subgraphs. In A. Brandstädt, K. Jansen, & R. Reischuk (Eds.), Graph-theoretic concepts in computer science : 39th International Workshop, WG 2013, 19-21 June 2013, Lübeck, Germany ; revised papers (201-212). https://doi.org/10.1007/978-3-642-45043-3_18
Conference Name | 39th International Workshop, WG 2013 |
---|---|
Conference Location | Lübeck, Germany |
Publication Date | Jan 1, 2013 |
Deposit Date | Dec 20, 2014 |
Publicly Available Date | Mar 28, 2024 |
Pages | 201-212 |
Series Title | Lecture notes in computer science |
Series Number | 8165 |
Series ISSN | 0302-9743,1611-3349 |
Book Title | Graph-theoretic concepts in computer science : 39th International Workshop, WG 2013, 19-21 June 2013, Lübeck, Germany ; revised papers. |
ISBN | 9783642450426 |
DOI | https://doi.org/10.1007/978-3-642-45043-3_18 |
Public URL | https://durham-repository.worktribe.com/output/1153569 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-45043-3_18
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