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On the parameterized complexity of coloring graphs in the absence of a linear forest

Couturier, J.F.; Golovach, P.A.; Kratsch, D.; Paulusma, D.

On the parameterized complexity of coloring graphs in the absence of a linear forest Thumbnail


Authors

J.F. Couturier

P.A. Golovach

D. Kratsch



Abstract

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}L(u)⊆{1,…,k}. Let PnPn denote the path on n vertices, and G+HG+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. We show that Listk-Coloring is fixed-parameter tractable on graphs with no induced rP1+P2rP1+P2 when parameterized by k+rk+r, and that for any fixed integer r, the problem k-Coloring restricted to such graphs allows a polynomial kernel when parameterized by k. Finally, we show that Listk-Coloring is fixed-parameter tractable on graphs with no induced P1+P3P1+P3 when parameterized by k.

Citation

Couturier, J., Golovach, P., Kratsch, D., & Paulusma, D. (2012). On the parameterized complexity of coloring graphs in the absence of a linear forest. Journal of discrete algorithms, 15, 56-62. https://doi.org/10.1016/j.jda.2012.04.008

Journal Article Type Article
Publication Date Aug 1, 2012
Deposit Date Mar 11, 2013
Publicly Available Date Apr 17, 2013
Journal Journal of Discrete Algorithms
Print ISSN 1570-8667
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 15
Pages 56-62
DOI https://doi.org/10.1016/j.jda.2012.04.008
Keywords k-Coloring, Listk-Coloring, H-free, Linear forest, Fixed-parameter tractable.
Public URL https://durham-repository.worktribe.com/output/1466804

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of discrete algorithms. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of discrete algorithms, 15, 2012, 10.1016/j.jda.2012.04.008





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