Lift-and-project cuts and perfect graphs

We analyze the application of lift-and-project to the clique relaxation of the stable set polytope. We characterize all the inequalities that can be generated through the application of the lift-and-project procedure, introduce the concept of 1-perfection and prove its equivalence to minimal imperfection. This characterization of inequalities and minimal imperfection leads to a generalization of the Perfect Graph Theorem of Lovász, as proved by Aguilera et al.