Two-edge connected spanning subgraphs and polyhedra

This paper studies the problem of finding a two-edge connected spanning subgraph of minimum weight. This problem is closely related to the widely studied traveling salesman problem and has applications to the design of reliable communication and transportation networks. We discuss the polytope associated with the solutions to this problem. We show that when the graph is series-parallel, the polytope is completely described by the trivial constraints and the so-called cut constraints. We also give some classes of facet defining inequalities of this polytope when the graph is general.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and CP Rail and the German Research Association (Deutsche Forschungsgemeinschaft SFR 303).