Facets of an assignment problem with 0-1 side constraint

We show that the problem of finding a perfect matching satisfying a single equality constraint with a 0-1 coefficients in an n x n incomplete bipartit e graph, polynomially reduces to a special case of the same peoblem called the partitioned case. Finding a solution matching for the partitioned case in the incomlpete bipartite graph, is equivalent to minimizing a partial su m of the variables over Q(n1,n2)(n,r1) = the convex hull of incidence vecto rs of solution matchings for the partitioned case in the complete bipartite graph. An important strategy to solve this minimization problem is to deve lop a polyhedral characterization of Q(n1,n2)(n,r1). Towards this effort, w e present two large classes of valid inequalities for Q(n1,n2)(n,r1), which are proved to be facet inducing using a facet lifting scheme.