On k-edge-connected Polyhedra: Box-TDIness in Series-Parallel Graphs

Given a connected graph G=(V,E) and an integer (formula presented), the connected graph H=(V,F) where F is a family of elements of E, is a k-edge-connected spanning subgraph of G if H remains connected after the removal of any k-1 edges. The convex hull of the k-edge-connected spanning subgraphs of a graph G forms the k-edge-connected spanning 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.