Polynomial-Delay Enumeration of Large Maximal Matchings

Abstract

We present polynomial-delay enumeration algorithms for maximal matchings with cardinality at least given threshold t. The first algorithm enumerates all such matchings in O(m²) delay, where m is the number of edges of an input graph. This extends known results for enumerating maximal matchings to the cardinality constrained problem. The second algorithm enumerates all maximal matchings in non-ascending order of its cardinality and runs in polynomial delay.