t-perfection is always strong for claw-free graphs

Abstract

A connected graph G is called t-perfect if its stable set polytope is determined by the non-negativity, edge and odd-cycle inequalities. More- over, G is called strongly t-perfect if this system is totally dual inte- gral. It is an open problem whether t-perfection is equivalent to strong t-perfection. We prove the equivalence for the class of claw-free graphs.