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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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.
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Dates et versions

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

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