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
Type
Article accepté pour publication ou publiéDate
2012Journal name
Discrete MathematicsVolume
312Number
7Publisher
Elsevier
Pages
1372-1385
Publication identifier
Metadata
Show full item recordAuthor(s)
Ries, BernardLaboratoire 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 colouringRelated items
Showing items related by title and author.
-
Lozin, Vadim; Raman, Rajiv; Ries, Bernard; Dabrowski, Konrad Kazimierz (2010) Communication / Conférence
-
Ries, Bernard; Monnot, Jérôme; Lozin, Vadim (2015) Article accepté pour publication ou publié
-
Lozin, Vadim; Monnot, Jérôme; Ries, Bernard (2013) Communication / Conférence
-
Paulusma, Daniël; Picouleau, Christophe; Ries, Bernard (2019) Article accepté pour publication ou publié
-
AbouEisha, Hassan; Hussain, Shahid; Lozin, Vadim; Monnot, Jérôme; Ries, Bernard; Zamaraev, Viktor (2018) Article accepté pour publication ou publié