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), SV is a dominating set if every vVS 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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