No cuts are necessary for minimum-weight bipartite matching as the constraint matrix is totally unimodular. Total unimodularity guarantees that any optimal basic solution is an integer solution.
Moreover, well-known algorithms for linear programming like simplex and primal-dual methods have straightforward (and illuminating!) combinatorial interpretations when restricted to minimum-weight bipartite matching.
Moreover, well-known algorithms for linear programming like simplex and primal-dual methods have straightforward (and illuminating!) combinatorial interpretations when restricted to minimum-weight bipartite matching.