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

Shmuel Friedland; Daniel Levy

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

Shmuel Friedland·Daniel Levy

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Abstract

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.

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BibTeX RIS

Shmuel Friedland, Daniel Levy. 2006-07-28. A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs. https://arxiv.org/abs/cs/0607135

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