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Colouring vertices of triangle-free graphs without forests

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Date
2012
Dewey
Principes généraux des mathématiques
Sujet
Clique-width; Polynomial-time algorithm; Triangle-free graphs; Vertex colouring
Journal issue
Discrete Mathematics
Volume
312
Number
7
Publication date
2012
Article pages
1372-1385
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.disc.2011.12.012
URI
https://basepub.dauphine.fr/handle/123456789/8185
Collections
  • LAMSADE : Publications
Metadata
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Author
Ries, Bernard
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Raman, Rajiv
Lozin, Vadim
Dabrowski, Konrad Kazimierz
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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