Perfectly contractile graphs and quadratic stable-set ideals

Let $G$ be a perfect graph, let ${\rm STAB}(G)$ be its stable set polytope, and let $I_{{\rm STAB}(G)}$ be the associated toric ideal. A graph is perfectly contractile in the sense used by the source.

Perfect-contractility conjecture. The following conditions are equivalent:

• $G$ is perfectly contractile;
• $I_{{\rm STAB}(G)}$ is quadratic;
• $G$ contains no even antiholes and no odd prisms.

This conjecture links a graph-theoretic structural property with quadratic generation of a stable-set toric ideal. The source introduces it as an open conjecture and supplies no resolution evidence.