A Simple Algorithm for Maximum Matching of Graphs

Abstract

Most maximum matching algorithms follow the approach of Edmonds ([1],[2]); usually they are rather complicated due to the necessity of shrinking and expanding “blossoms”. In this paper algorithms are presented which construct maximum matchings without making use of “blossoms”. The first algorithm which labels the “even” nodes of Edmonds relative to a free node v performs a depth-first-search and occasionally contracts triples of vertices. The second algorithm constructs for a given even node w an edge set H which turns out to be an alternating path of even length from v to w by adding successively certain pairs of edges.