Error Banner.fade_out.modal_overlay.modal_overlay .modal_wrapper.modal_overlay [email protected](max-width:630px)@media(max-width:630px).modal_overlay .modal_fixed_close.modal_overlay .modal_fixed_close:before.modal_overlay .modal_fixed_close:before.modal_overlay .modal_fixed_close:before.modal_overlay .modal_fixed_close:hover:before.Selector .selector_input_interaction .selector_input. Selector .selector_input_interaction .selector_spinner. Your personality needs to shine through, and it’s hard to do that if you’re nervous, out of practice at writing, and unsure what to share.If, for every vertex in a graph, there is a near-perfect matching that omits only that vertex, the graph is also called factor-critical.Given a matching M, One can prove that a matching is maximum if and only if it does not have any augmenting path.A perfect matching can only occur when the graph has an even number of vertices.A near-perfect matching is one in which exactly one vertex is unmatched.A perfect matching is also a minimum-size edge cover.Thus, , that is, the size of a maximum matching is no larger than the size of a minimum edge cover.

Finding a matching in a bipartite graph can be treated as a network flow problem.

If the graph is not complete bipartite, missing edges are inserted with value zero.

Finding such a matching is known as the assignment problem.

The Hungarian algorithm solves the assignment problem and it was one of the beginnings of combinatorial optimization algorithms.

It uses a modified shortest path search in the augmenting path algorithm.