Lift-and-project ranks of the stable set polytope of joined a-perfect graphs

TL;DR

This paper investigates the lift-and-project ranks of the stable set polytope for joined a-perfect graphs, providing exact ranks for webs and antiwebs, and establishing bounds for broader graph classes.

Contribution

It computes the disjunctive rank of webs and antiwebs and extends these results to joined a-perfect graphs, advancing understanding of polyhedral operators in graph theory.

Findings

Disjunctive rank of all webs and antiwebs is computed.

Bounds for disjunctive rank in joined a-perfect graphs are established.

Results contribute to understanding the complexity of separation problems.

Abstract

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.