Box-total dual integrality and edge-connectivity

Abstract

Given a graph $$G=(V,E)$$ and an integer $$k\ge 1$$ , the graph $$H=(V,F)$$ , where F is a family of elements (with repetitions allowed) of E, is a k-edge-connected spanning subgraph of G if H cannot be disconnected by deleting any $$k-1$$ elements of F. The convex hull of incidence vectors of the k-edge-connected subgraphs of a graph G forms the k-edge-connected subgraph polyhedron of G. We prove that this polyhedron is box-totally dual integral if and only if G is series–parallel. In this case, we also provide an integer box-totally dual integral system describing this polyhedron.