The stable set polytope of claw-free graphs with stability number at least four. II. Striped graphs are G-perfect

In [6], Edmonds provided the first complete description of the polyhedron associated with a combinatorial optimization problem: the matching polytope. As the matching problem is equivalent to the stable set problem on line graphs, many researchers tried to generalize Edmonds' result by considering the stable set problem on a superclass of line graphs: the claw-free graphs. However, as testified also by Grotschel, Lovasz, and Schrijver [14], "in spite of considerable efforts, no decent system of inequalities describing STAB(G) for claw-free graphs is known". Here, we provide an explicit linear description of the stable set polytope of claw-free graphs with stability number at least four and with no 1-join.