Dabrowski, Konrad K., Lozin, Vadim, Raman, Rajiv and Ries, Bernard. (2012) Colouring vertices of triangle-free grapshs without forest. Discrete Mathematics, Vol. 312 (No. 7). pp. 1372-1385. ISSN 0012365X

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Abstract

The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it is NP-complete in any subclass of triangle-free graphs defined by a finite collection of forbidden induced subgraphs, each of which contains a cycle. In this paper, we study the vertex colouring problem in subclasses of triangle-free graphs obtained by forbidding graphs without cycles, i.e., forests, and prove polynomial-time solvability of the problem in many classes of this type. In particular, our paper, combined with some previously known results, provides a complete description of the complexity status of the problem in subclasses of triangle-free graphs obtained by forbidding a forest with at most 6 vertices.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Discrete Mathematics
Publisher:	Elsevier BV
ISSN:	0012365X
Date:	2012
Volume:	Vol. 312
Number:	No. 7
Page Range:	pp. 1372-1385
Identification Number:	10.1016/j.disc.2011.12.012
Status:	Peer Reviewed
URI:	http://wrap.warwick.ac.uk/id/eprint/44754

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