On Minimum Dominating Sets in cubic and (claw,H)-free graphs - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

On Minimum Dominating Sets in cubic and (claw,H)-free graphs

Abstract

Given a graph $G=(V,E)$, $S\subseteq V$ is a dominating set if every $v\in V\setminus S$ is adjacent to an element of $S$. The Minimum Dominating Set problem asks for a dominating set with minimum cardinality. It is well known that its decision version is $NP$-complete even when $G$ is a claw-free graph. We give a complexity dichotomy for the Minimum Dominating Set problem for the class of $(claw, H)$-free graphs when $H$ has at most six vertices. In an intermediate step we show that the Minimum Dominating Set problem is $NP$-complete for cubic graphs.
Fichier principal
Vignette du fichier
2002.12232.pdf (477.16 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02493931 , version 1 (18-03-2020)

Identifiers

Cite

Valentin Bouquet, François Delbot, Christophe Picouleau, Stephane Rovedakis. On Minimum Dominating Sets in cubic and (claw,H)-free graphs. 2020. ⟨hal-02493931⟩
152 View
177 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More