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arXiv · 1402.6190

Approximate Counting of Matchings in $(3,3)$-Hypergraphs

Andrzej Dudek·Marek Karpinski·Andrzej Ruciński·Edyta Szymańska
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Abstract

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite $(3,3)$-hypergraphs. The proof technique of this paper uses the general correlation decay technique and a new combinatorial analysis of the underlying structures of the intersection graphs. The proof method could be also of independent interest.

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Andrzej Dudek, Marek Karpinski, Andrzej Ruciński, Edyta Szymańska. 2017-10-25. Approximate Counting of Matchings in $(3,3)$-Hypergraphs. https://arxiv.org/abs/1402.6190

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