Skip to Main content Skip to Navigation

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

Valentin Bouquet 1, 2 François Delbot 3 Christophe Picouleau 1 Stephane Rovedakis 2
1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
2 CEDRIC - ROC - CEDRIC. Réseaux et Objets Connectés
CEDRIC - Centre d'études et de recherche en informatique et communications
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.
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02493931
Contributor : Valentin Bouquet <>
Submitted on : Wednesday, March 18, 2020 - 6:07:46 PM
Last modification on : Thursday, March 19, 2020 - 12:13:26 PM

File

2002.12232.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02493931, version 1
  • ARXIV : 2002.12232

Citation

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

Share

Metrics

Record views

42

Files downloads

4