Polynomial Algorithms for the Maximum Stable Set Problem on Particular Classes of P_5-Free Graphs

Abstract The Maximum Stable Set Problem (MS) is a well-known NP-hard problem. A popular research stream considers classes of graphs, defined in terms of forbidden subgraphs, in which either MS is NP-hard or can be solved by polynomial algorithms. In this paper we focus on three of these classes: in one of them, MS is still NP-hard; in the others, the problem difficulty is an open question. However, for those graphs in such classes that have no induced paths with five vertices ( P 5 ) the problem becomes solvable in polynomial time. Whether MS is difficult or not in the class of P 5 -free graphs is still open.