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arXiv · 1911.10986

On Perfect Matchings in $k$-complexes

Jie Han
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Abstract

Keevash and Mycroft [\emph{Mem.~Amer.~Math.~Soc., 2015}] developed a geometric theory for hypergraph matchings and characterized the dense simplicial complexes that contain a perfect matching. Their proof uses the hypergraph regularity method and the hypergraph blow-up lemma recently developed by Keevash. In this note we give a new proof of their results, which avoids these complex tools. In particular, our proof uses the lattice-based absorbing method developed by the author and a recent probabilistic argument of Kohayakawa, Person and the author.

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Jie Han. 2019-11-21. On Perfect Matchings in $k$-complexes. https://arxiv.org/abs/1911.10986

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