Domination, coloring and stability in P5-reducible graphs
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 $k$).