On the stable set problem in special P5-free graphs Original Research Article

The complexity status of the stable set problem in P5-free graphs remains an open question for a long time in spite of a lot of particular results in this direction. The purpose of the present paper is to summarize these results and to propose several new ones. In particular, we prove that the problem of finding a maximum stable set can be solved in polynomial time in the class of (P5,Km,m)-free graphs for any fixed m.