P₅-Free Augmenting Graphs and the Maximum Stable Set Problem

The complexity status of the maximum stable set problem in the class of P₅-free graphs is unknown. In this paper, we first propose a characterization of all connected P₅-free augmenting graphs. We then use this characterization to detect families of subclasses of P₅-free graphs where the maximum stable set problem has a polynomial time solution. These families extend several previously studied classes.