A recursive algorithm for Finding all perfect pair matchings in complete graphs

A recursive algorithm for Finding all perfect pair matchings in complete graphs

Perfect pair matching is one of well-known problems in mathematics and graph theory. Hungarian algorithm is an algorithm that produces all perfect pair matching in graph and its computational order is O(V*E) where V shows the number of vertexes and E shows the number of edges. In this paper, we propose a new algorithm to find all perfect pair matching in a complete graph. This algorithm generates all perfect pair matching recursively. In the proof section we prove that this algorithm has O(n!!) computational order.