t-PERFECTION IS ALWAYS STRONG FOR CLAW-FREE GRAPHS

摘要

A connected graph G is called t-perfect if its stable set polytope is determined by the nonnegativity, edge, and odd-cycle inequalities. Moreover, G is called strongly t-perfect if this system is totally dual integral. 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.