Rainbow perfect matchings for 4-uniform hypergraphs

Abstract

Let $n$ be a sufficiently large integer with $n\equiv 0(\mathrm{mod}4)$ and let $F_i\subseteq \left(\genfrac{}{}{0ex}{}{[n]}{4}\right)$ where $i\in [n/4]$. We show that if each vertex of $F_i$ is contained in more than $\left(\genfrac{}{}{0ex}{}{n-1}{3}\right)-\left(\genfrac{}{}{0ex}{}{3n/4}{3}\right)$ edges, then $\{F_1,\dots ,F_{n/4}\}$ admits a rainbow matching, i.e., a set of $n/4$ edges consisting of one edge from each $F_i$. This generalizes a deep result of Khan on perfect matchings in 4-uniform hypergraphs.

arXiv commentarXiv admin note: text overlap with arXiv:2004.12561

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Cited by in corpus (1)

• Co-degree threshold for rainbow perfect matchings in uniform hypergraphs