Domination, coloring and stability in P5P5-reducible graphs

A graph GG is P5P5-reducible   if every vertex of GG lies in at most one induced P5P5 (path on five vertices). We show that a number of interesting results concerning P5P5-free graphs can be extended to P5P5-reducible graphs, namely: the existence of a dominating clique or P3P3, the fact that kk-colorability can be decided in polynomial time (for fixed kk), and the fact that a maximum stable set can be found in polynomial time in the class of kk-colorable P5P5-reducible graphs (for fixed kk).