A polyhedron with all s-t cuts as vertices, and adjacency of cuts

Consider the polyhedron represented by the dual of the LP formulation of the maximum s-t flow problem. It is well known that the vertices of this polyhedron are integral, and can be viewed as s-t cuts in the given graph. In this paper, the authors show that not all s-t cuts appear as vertices, and we give a characterization. They also characterize pairs of cuts that form edges of this polyhedron. Finally, the authors show a set of inequalities such that the corresponding polyhedron has as its vertices all s-t cuts.