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The problem of computing a maximum weight matching in a bipartite graph is one of the fundamental algorithmic problems that has played an important role in the development of combinatorial optimization and algorithmics. Let Gw,σ is a collection of all weighted bipartite graphs, each having σ and w as the size of each of the non-empty subset of the vertex partition and the total weight of the graph, respectively. We give a tight lower bound dw−σ σ e + 1 for the set {Wt(mwm(G)) | G ∈ Gw,σ} which denotes the collection of weights of maximum weight bipartite matchings of all the graphs in Gw,σ.

An Optimum Lower Bound for the Weights of Maximum Weight Matching in Bipartite Graphs