Domination, coloring and stability in P5-reducible graphs - Archive ouverte HAL
Article Dans Une Revue Discrete Applied Mathematics Année : 2015

Domination, coloring and stability in P5-reducible graphs

Frédéric Maffray

Résumé

A graph $G$ is \emph{$P_5$-reducible} if every vertex of $G$ lies in at most one induced $P_5$ (path on five vertices). We show that a number of interesting results concerning $P_5$-free graphs can be extended to $P_5$-reducible graphs, namely: the existence of a dominating clique or $P_3$, the fact that $k$-colorability can be decided in polynomial time (for fixed $k$), and the fact that a maximum stable set can be found in polynomial time in the class of $k$-colorable $P_5$-reducible graphs (for fixed $k$).
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Dates et versions

hal-01212179 , version 1 (06-10-2015)

Identifiants

  • HAL Id : hal-01212179 , version 1

Citer

Jean-Luc Fouquet, Frédéric Maffray. Domination, coloring and stability in P5-reducible graphs. Discrete Applied Mathematics, 2015, 184, pp.122-129. ⟨hal-01212179⟩
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