Article Dans Une Revue Theoretical Computer Science Année : 2024

On the complexity of Dominating Set for graphs with fixed diameter

Résumé

A set S⊆V of a graph G=(V,E) is a dominating set if each vertex has a neighbor in S or belongs to S. Dominating Set is the problem of deciding, given a graph G and an integer k≥1, if G has a dominating set of size at most k. It is well known that this problem is NP-complete even for claw-free graphs. We give a (almost) complexity dichotomy for Dominating Set for the class of claw-free graphs with diameter d. We show that the problem is NP-complete for every fixed d≥3 and polynomial-time solvable for d≤2. To prove the case d=2, we show that Minimum Maximal Matching can be solved in polynomial-time for 2K2-free graphs.

Fichier principal
Vignette du fichier
2304.09701v1.pdf (434.34 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Licence

Dates et versions

hal-04549484 , version 1 (27-06-2025)

Licence

Identifiants

Citer

Valentin Bouquet, François Delbot, Christophe Picouleau, Stephane Rovedakis. On the complexity of Dominating Set for graphs with fixed diameter. Theoretical Computer Science, 2024, 1001, pp.114561. ⟨10.1016/j.tcs.2024.114561⟩. ⟨hal-04549484⟩
495 Consultations
181 Téléchargements

Altmetric

Partager

  • More