Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
Selected topics on assignment problems
Discrete Applied Mathematics
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The classical conditions of the existence of a perfect matching in bipartite graphs are used directly or indirectly to solve the assignment problem by the well-known algorithms. In the paper, we define a vector and an extended polymatroid for a bipartite graph so that the bipartite graph has a perfect matching if and only if the vector is the basis of the extended polymatroid.