A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs
<|reference_start|>A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs: 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   $G_k$ on an even number of vertices divided by a suitable factor.   If $G$ is bipartite then one can construct a bipartite $G_k$.   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.<|reference_end|>
@article{friedland2006a,
    title={A polynomial-time approximation algorithm for the number of k-matchings
  in bipartite graphs},
    author={Shmuel Friedland and Daniel Levy},
    journal={arXiv preprint arXiv:cs/0607135},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0607135},
    primaryClass={cs.CC cs.DM}
}