 Take a complete graph with 6 vertices, K6.It has 15 edges, which can be partitioned into 3-edge perfect matchings in 15 different ways.Finally, it is possible to find a set of 5 perfect matchings from the set of 15 such that no two matchings share an edge, and that between them include all edges of the graph; this graph factorization can be done in 6 different ways.