A note on contracting claw-free graphs

Abstract : A graph containment problem is to decide whether one graph called the host graph can be modified into some other graph called the target graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible graph operations permitted. By allowing any combination of these four operations we capture the following problems: testing on (induced) minors, (induced) topological minors, (induced) subgraphs, (induced) spanning subgraphs, dissolutions and contractions. We show that these problems stay NP-complete even when the host and target belong to the class of line graphs, which form a subclass of the class of claw-free graphs, i.e., graphs with no induced 4-vertex star. A natural question is to study the computational complexity of these problems if the target graph is assumed to be fixed. We show that these problems may become computationally easier when the host graphs are restricted to be claw-free. In particular we consider the problems that are to test whether a given host graph contains a fixed target graph as a contraction.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 2 (2), pp.223--232
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00980769
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : vendredi 18 avril 2014 - 16:43:56
Dernière modification le : jeudi 7 septembre 2017 - 01:03:46
Document(s) archivé(s) le : lundi 10 avril 2017 - 15:38:21

Fichier

2128-8288-1-PB.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00980769, version 1

Collections

Citation

Jiří Fiala, Marcin Kamiński, Daniël Paulusma. A note on contracting claw-free graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 2 (2), pp.223--232. 〈hal-00980769〉

Partager

Métriques

Consultations de la notice

670

Téléchargements de fichiers

145