Perfectly contractile graphs and quadratic toric rings

Perfect graphs form one of the distinguished classes finite simple graphs. In 2006, Chudnovsky, Robertson, Seymour and Thomas proved that a graph is perfect if only it has no odd holes antiholes as induced subgraphs, which was conjectured by Berge. We consider class ${\mathcal A}$ have holes, stretchers subgraphs. particular, every belonging to perfect. Everett Reed belongs perfectly contractile. present paper, we discuss from viewpoint commutative algebra. fact, conjecture $G$ toric ideal stable set polytope generated quadratic binomials. Especially, show this true for Meyniel graphs, orderable clique separable are contractile