Algorithms for enumerating all perfect, maximum and maximal matchings in bipartite graphs

Abstract

For a bipartite graph G = (V, E), (1) perfect, (2) maximum and (3) maximal matchings are matchings (1) such that all vertices are incident to some matching edges, (2) whose cardinalities axe maximum among all matchings, (3) which axe contained in no other matching. In this paper, we present three algorithms for enumerating these three types of matchings. Their time complexities axe o(IvI) per a matching.