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The stable set polytope of a graph $G$, denoted as STAB($G$), is the convexhull of all the incidence vectors of stable sets of $G$. To describe a linearsystem which defines STAB($G$) seems to be a difficult task in the generalcase. In this paper we present a complete description of the stable setpolytope of ($P_6$,triangle)-free graphs (and more generally of($P_6$,paw)-free graphs). For that we combine different tools, in the contextof a well known result of Chv\'atal \cite{Chvatal1975} which allows to focusjust on prime facet-inducing graphs, with particular reference to a structureresult on prime ($P_6$,triangle)-free graphs due to Brandst\"adt et al.\cite{BraKleMah2005}. Also we point out some peculiarities of newfacet-inducing graphs detected along this study with the help of a software.

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