A note on the disjunctive index of joined a-perfect graphs

In this paper we present a lower bound of the disjunctive rank of the facets describing the stable set polytope of joined a-perfect graphs. This class contains near-bipartite, t-perfect, h-perfect and complement of fuzzy interval graphs, among others. The stable set polytope of joined a-perfect graphs is described by means of full rank constraints of its node induced prime antiwebs. As a first step, we completely determine the disjunctive rank of all these constraints. Using this result we obtain a lower bound of the disjunctive index of joined a-perfect graphs and prove that this bound can be achieved. In addition, we completely determine the disjunctive index of every antiweb and observe that it does not always coincide with the disjunctive rank of its full rank constraint.