Perfectly matchable subgraph problem on a bipartite graph
We consider the maximum weight perfectly matchable subgraph problem on a bipartite graph with respect to given nonnegative weights of its edges. We show that has a perfect matching if and only if some vector indexed by the nodes in is a base of an extended polymatroid associated with a submodular function defined on the subsets of . The dual problem of the separation problem for the extended polymatroid is transformed to the special maximum flow problem on . In this paper, we give a linear programming formulation...