The stable set polytope of icosahedral graphs

Here we show that another important class of claw-free graphs with stability number three belongs to this set: the class of icosahedral graphs, named S1 by Chudnovsky and Seymour (2008). In particular, we prove that the stable set polytope of icosahedral graphs is described by: rank, lifted 5-wheel and lifted wedge inequalities, and all these linear inequalities have coefficients in {0,1,2}.