Colouring vertices of triangle-free graphs without forests
Ries, Bernard; Raman, Rajiv; Lozin, Vadim; Dabrowski, Konrad Kazimierz (2012), Colouring vertices of triangle-free graphs without forests, Discrete Mathematics, 312, 7, p. 1372-1385. 10.1016/j.disc.2011.12.012
TypeArticle accepté pour publication ou publié
Journal nameDiscrete Mathematics
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Dabrowski, Konrad Kazimierz
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.
Subjects / KeywordsClique-width; Polynomial-time algorithm; Triangle-free graphs; Vertex colouring
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