Graph G is bipartite graph, I want to just count number of perfect matching. Is there any algorithm exist using combinatorial+graph theory, by which i cant count this. I tried by traversing the graph, but as there are so many possibilities and I just want number of perfect matching I asked here.
My actual question is to find the number of transversal given a collection of set ...  After a little bit of study it has come down to:  How can we count the number of matchings in a bipartite graph with parts of size $m$ and $n$ such that it covers all $m$ vertices of the first part, $m \le n$?  I already know that there is a way to count the number of perfect matchings in a bipartite graph with $m=n$ using the permanent of its (square) incidence matrix.
My actual question is to find the number of transversal given a collection of set ...  After a little bit of study it has come down to:  How can we count the number of matchings in a bipartite graph with parts of size $m$ and $n$ such that it covers all $m$ vertices of the first part, $m \le n$?  I already know that there is a way to count the number of perfect matchings in a bipartite graph with $m=n$ using the permanent of its (square) incidence matrix.