Domination, coloring and stability in P5-reducible graphs

A graph G is 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 ).