The perfectly Matchable Subgraph Polytope of an arbitrary graph

The Perfectly Matchable Subgraph Polytope of a graphG=(V, E), denoted byPMS(G), is the convex hull of the incidence vectors of thoseXV which induce a subgraph having a perfect matching. We describe a linear system whose solution set isPMS(G), for a general (nonbipartite) graphG. We show how it can be derived via a projection technique from Edmonds' characterization of the matching polytope ofG. We also show that this system can be deduced from the earlier bipartite case 2], by using the Edmonds-Gallai structure theorem. Finally, we characterize which inequalities are facet inducing forPMS(G), and hence essential.