On the directed cut cone and polytope

In this paper we study the directed cut cone and polytope which are the positive hull and convex hull of all directed cut vectors of a complete directed graph, respectively. We present results on the polyhedral structure of these polyhedra. A relation between directed cut polyhedra and undirected cut polyhedra is established that provides families of facet defining inequalities for directed cut polyhedra from those known for undirected cut polyhedra.