Facets of the dynamic monopoly polytope: Linear ordering formulation

Abstract

We study the polyhedral structure of the monopoly polytope which arises from an integer programming formulation of dynamic monopolies in graphs. This formulation extends from the linear ordering polytope formulation. Several families of valid and facet defining inequalities are investigated. We show that (anti-) arborescences lead to families of strong valid inequalities each of which contains exponentially many facet defining inequalities. We also generalize the k-fence and Möbius ladder inequalities for the monopoly polytope.