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

Couturier, J.F. and Golovach, P.A. and Kratsch, D. and Paulusma, Daniel (2012) 'On the parameterized complexity of coloring graphs in the absence of a linear forest.', Journal of discrete algorithms., 15 . pp. 56-62.

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.

Item Type:Article
Keywords:k-Coloring, Listk-Coloring, H-free, Linear forest, Fixed-parameter tractable.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.jda.2012.04.008
Publisher 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
Date accepted:No date available
Date deposited:17 April 2013
Date of first online publication:August 2012
Date first made open access:No date available

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