The stable set polytope of ($P_6$, triangle)-free graphs and new facet-inducing graphs

The stable set polytope of a graph G, denoted as STAB(G), is the convex hull of all the incidence vectors of stable sets of G. To describe a linear system which defines STAB(G) seems to be a difficult task in the general case. In this paper we present a complete description of the stable set polytope of (P6,triangle)-free graphs (and more generally of (P6,paw)-free graphs). For that we combine different tools, in the context of a well known result of Chvátal [6] which allows to focus just on prime facet-inducing graphs, with particular reference to a structure result on prime (P6,triangle)-free graphs due to Brandstädt et al. [4]. Also we point out some peculiarities of new facet-inducing graphs detected along this study with the help of a software.