Matchings

Abstract

This chapter is devoted to the problem of finding maximal matchings in arbitrary graphs; the bipartite case was treated in Section 7.2. Contrary to the bipartite case, the general case cannot be reduced immediately to a flow problem. However, we will see that the notion of an augmenting path can be modified appropriately. Kocay and Stone (1993) and Kocay and Stone (1995) showed that matchings can be treated in the context of Flow Theory by introducing special networks and flows satisfying certain symmetry conditions. Subsequently, Fremuth-Paeger and Jungnickel (1998a, 1998b, 1998c, 1998d, 1998e) provided a general theory based on this approach, including efficient algorithms. We will not present this rather involved theory because it would take up too much space, and refer the reader to the original sources instead.