Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited

We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds’ primal-dual algorithm for the maximum weighted matching problem.