Acyclic colourings of graphs with bounded degree

Abstract : A k-colouring of a graph G is called acyclic if for every two distinct colours i and j, the subgraph induced in G by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, there are no bichromatic alternating cycles. In 1999 Boiron et al. conjectured that a graph G with maximum degree at most 3 has an acyclic 2-colouring such that the set of vertices in each colour induces a subgraph with maximum degree at most 2. In this paper we prove this conjecture and show that such a colouring of a cubic graph can be determined in polynomial time. We also prove that it is an NP-complete problem to decide if a graph with maximum degree 4 has the above mentioned colouring.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (1), pp.59-74
Liste complète des métadonnées

Littérature citée [9 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00990426
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : mardi 13 mai 2014 - 15:36:16
Dernière modification le : mercredi 29 novembre 2017 - 10:26:17
Document(s) archivé(s) le : lundi 10 avril 2017 - 22:04:51

Fichier

1013-4938-1-PB.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00990426, version 1

Collections

Citation

Mieczyslaw Borowiecki, Anna Fiedorowicz, Katarzyna Jesse-Jozefczyk, Elzbieta Sidorowicz. Acyclic colourings of graphs with bounded degree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (1), pp.59-74. 〈hal-00990426〉

Partager

Métriques

Consultations de la notice

76

Téléchargements de fichiers

264