  In this paper we study lift-and-project polyhedral operators defined by
Lov?asz and Schrijver and Balas, Ceria and Cornu?ejols on the clique relaxation
of the stable set polytope of web graphs. We compute the disjunctive rank of
all webs and consequently of antiweb graphs. We also obtain the disjunctive
rank of the antiweb constraints for which the complexity of the separation
problem is still unknown. Finally, we use our results to provide bounds of the
disjunctive rank of larger classes of graphs as joined a-perfect graphs, where
near-bipartite graphs belong.
