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A matching on a graph is a set of edges, no two of which share a vertex. A maximum matching contains the greatest number of edges possible. This paper presents an efficient implementation of Edmonds' algorithm for finding a maximum matching. The computation time is proportional to V3, where V is the number of vertices; previous implementations of Edmonds' algorithm have computation time proportional to V4. The implementation is based on a system of labels that encodes the structure of alternating paths.

An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs