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arXiv · 1911.07431

Near perfect matchings in uniform hypergraphs

Hongliang Lu·Xingxing Yu·Xiaofan Yuan
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Abstract

In this paper, we study degree conditions for the existence of large matchings in uniform hypergraphs. We prove that for integers $k,l,n$ with $k\ge 3$, $k/2 {n-l\choose k-l}-{(n-l)-(\lceil n/k \rceil-2)\choose 2}$, then $H$ has a matching covering all but a constant number of vertices. When $l=k-2$ and $k\ge 5$, such a matching is near perfect and our bound on $\delta_l(H)$ is best possible. When $k=3$, with the help of an absorbing lemma of H\'{a}n, Person, and Schacht, our proof also implies that $H$ has a perfect matching, a result proved by K\" uhn, Osthus, and Treglown and, independently, of Kahn.

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Hongliang Lu, Xingxing Yu, Xiaofan Yuan. 2019-11-18. Near perfect matchings in uniform hypergraphs. https://arxiv.org/abs/1911.07431

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