The most vital edges of matching in a bipartite graph

Let G = (V,E) be an undirected graph having an edge weight we ≥ 0 for each e ϵ E. An edge is called a most vital edge (with respect to weighted matching) if its removal from G results in the largest decrease in the total weight of the maximum weighted matching. In this paper, we study the most vital edges of matching in a weighted bipartite graph. We present an O(n3) algorithm to obtain the most vital edges. © 1993 by John Wiley & Sons, Inc.