The Chvátal closure of generalized stable sets in bidirected graphs

Abstract

Abstract We consider the set of integral solutions of A x ⩽ b , x ⩾ 0 , where A is the edge-vertex incidence matrix of a bidirected graph. We characterize its corner polyhedron, i.e. the convex hull of the points satisfying all the constraints except the non-negativity of the basic variables. We show that the non-trivial inequalities necessary to describe this polyhedron can be derived as fractional Gomory cuts. It follows in particular that the split closure is equal to the Chvatal closure in this case.