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Colouring vertices of triangle-free grapshs without forest
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Dabrowski, Konrad K., Lozin, Vadim V., Raman, Rajiv and Ries, Bernard (2012) Colouring vertices of triangle-free grapshs without forest. Discrete Mathematics, Vol. 312 (No. 7). pp. 1372-1385. doi:10.1016/j.disc.2011.12.012 ISSN 0012365X.
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Official URL: http://dx.doi.org/10.1016/j.disc.2011.12.012
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 | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Discrete Mathematics | ||||
Publisher: | Elsevier BV | ||||
ISSN: | 0012365X | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol. 312 | ||||
Number: | No. 7 | ||||
Page Range: | pp. 1372-1385 | ||||
DOI: | 10.1016/j.disc.2011.12.012 | ||||
Status: | Peer Reviewed |
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