Colouring vertices of triangle-free graphs without forests

Ries, Bernard; Raman, Rajiv; Lozin, Vadim; Dabrowski, Konrad Kazimierz

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

Type

Article accepté pour publication ou publié

Date

2012

Journal name

Discrete Mathematics

Volume

312

Number

Publisher

Elsevier

Pages

1372-1385

Publication identifier

10.1016/j.disc.2011.12.012

Metadata

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Author(s)

Ries, Bernard
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Raman, Rajiv

Lozin, Vadim

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 / Keywords

Clique-width; Polynomial-time algorithm; Triangle-free graphs; Vertex colouring