A note on perfect matchings in uniform hypergraphs

Abstract

We determine the \emph{exact} minimum $\ell$-degree threshold for perfect matchings in $k$-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than $\frac{1}{2}\left(\genfrac{}{}{0ex}{}{n}{k-\ell }\right)$. This extends our previous results that determine the minimum $\ell$-degree thresholds for perfect matchings in $k$-uniform hypergraphs for all $\ell \ge k/2$ and provides two new (exact) thresholds: $(k,\ell )=(5,2)$ and $(7,3)$.

11 pages, final version

Cited by in corpus (1)

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