A Generalization of the Perfect Graph Theorem Under the Disjunctive Index

Abstract

In this paper, we relate antiblocker duality between polyhedra, graph theory, and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, 𝒦(G), of the stable set polytope in a graph G, and the one associated to its complementary graph, 𝒦(Ḡ). We obtain a generalization of the Perfect Graph Theorem, proving that the disjunctive indices of 𝒦(G) and 𝒦(Ḡ) always coincide.