Abstract
In this chapter we discuss the problem of finding a matching of maximal cardinality in a general (nonbipartite) graph G = (V, E). We will first introduce some combinatorial structures which typically arise in nonbipartite graphs and which have to be handled in cardinality matching algorithms. We also state the nonbipartite counterparts of the “existence theorems” and “characterizations” of perfect matchings in bipartite graphs. Then we present the alternating path labeling method for solving the cardinality matching problem in non-bipartite graphs.
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