The stable set polytope of claw-free graphs with large stability number

In this paper we give an explicit description of the stable set polytope of a claw-free graph obtained by repeated applications of the strip composition of fuzzy linear interval strips, fuzzy XX-strips, and fuzzy antihat strips. Using a decomposition theorem of Chudnovsky and Seymour, this allows us to describe the stable set polytope of all facet defining claw-free graphs with stability number greater than 3.