# A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs

@article{Friedland2006APA, title={A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs}, author={S. Friedland and Daniel Levy}, journal={ArXiv}, year={2006}, volume={abs/cs/0607135} }

We show that the number of k-matching in a given undirected graph G is equal to the number of perfect matching of the corresponding graph Gk on an even number of vertices divided by a suitable factor. If G is bipartite then one can construct a bipartite Gk. For bipartite graphs this result implies that the number of k-matching has a polynomial-time approximation algorithm. The above results are extended to permanents and hafnians of corresponding matrices.

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