4-Coloring H-free graphs when H is small

Golovach, P.A.; Paulusma, D.; Song, J.

doi:10.1016/j.dam.2012.08.022

4-Coloring H-free graphs when H is small

Golovach, P.A.; Paulusma, D.; Song, J.

Authors

P.A. Golovach

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

J. Song

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.

Citation

Golovach, P., Paulusma, D., & Song, J. (2013). 4-Coloring H-free graphs when H is small. Discrete Applied Mathematics, 161(1-2), 140-150. https://doi.org/10.1016/j.dam.2012.08.022

Journal Article Type	Article
Publication Date	Jan 1, 2013
Deposit Date	Mar 11, 2013
Publicly Available Date	Apr 17, 2013
Journal	Discrete Applied Mathematics
Print ISSN	0166-218X
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	161
Issue	1-2
Pages	140-150
DOI	https://doi.org/10.1016/j.dam.2012.08.022
Public URL	https://durham-repository.worktribe.com/output/1487663

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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