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4-Coloring H-free graphs when H is small.

Golovach, P.A. and Paulusma, Daniel and Song, J. (2013) '4-Coloring H-free graphs when H is small.', Discrete applied mathematics., 161 (1-2). pp. 140-150.

Abstract

The kk-Coloring problem is to test whether a graph can be colored with at most kk colors such that no two adjacent vertices receive the same color. If a graph GG does not contain a graph HH as an induced subgraph, then GG is called HH-free. For any fixed graph HH on at most six vertices, it is known that 33-Coloring is polynomial-time solvable on HH-free graphs whenever HH is a linear forest, and NP-complete otherwise. By solving the missing case P2+P3P2+P3, we prove the same result for 44-Coloring provided that HH is a fixed graph on at most five vertices.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.dam.2012.08.022
Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Discrete applied mathematics. 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 Discrete applied mathematics, 161, 1-2, 2013, 10.1016/j.dam.2012.08.022
Date accepted:No date available
Date deposited:17 April 2013
Date of first online publication:January 2013
Date first made open access:No date available

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