On the cut polytope

The cut polytopePC(G) of a graphG=(V, E) is the convex hull of the incidence vectors of all edge sets of cuts ofG. We show some classes of facet-defining inequalities ofPC(G). We describe three methods with which new facet-defining inequalities ofPC(G) can be constructed from known ones. In particular, we show that inequalities associated with chordless cycles define facets of this polytope; moreover, for these inequalities a polynomial algorithm to solve the separation problem is presented. We characterize the facet defining inequalities ofPC(G) ifG is not contractible toK5. We give a simple characterization of adjacency inPC(G) and prove that for complete graphs this polytope has diameter one and thatPC(G) has the Hirsch property. A relationship betweenPC(G) and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied.