On minimal imperfect graphs without induced P5

AbstractIn this paper, we summarize previous known results on P5-free minimal imperfect graphs (i.e. minimal imperfect graphs not containing a path on 5 vertices as induced subgraph) and we introduce two new classes of graphs (defined by a local property) that contain P5-free graphs. Next, we show that most of the results concerning P5-free graphs can be extended to these classes. Moreover, we present a structural characterization of these graphs which leads to some new results. In particular, we prove that the Strong Perfect Graph Conjecture holds true for P5-free and F-free graphs where F is any connected configuration on 5 vertices not containing an induced 2K2