A matching in a graph is a set of edges that have no common vertices. A maximum matching is a matching that contains the largest possible number of edges for a matching. It is possible that a graph contains several maximum matchings. The number of edges in a maximum matching is called the matching number of the graph. A perfect matching is a matching which covers all the vertices of the graph. The size of a perfect matching equals half of the order of the graph. Therefore a perfect matching is only possible in a graph containing an even number of vertices.