Rainbow Perfect Matchings for 4-Uniform Hypergraphs
Rainbow Perfect Matchings for 4-Uniform Hypergraphs
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DOI：
10.1137/21m1442383
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发表时间：
2021-05
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通讯作者：
Hongliang Lu;Yan Wang;Xingxing Yu
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作者：
Hongliang Lu;Yan Wang;Xingxing Yu
设$n$是一个足够大的整数，$n\equiv 0\pmod 4$，并设$F_i \subseteq{[n]\choose 4}$ where $i\in [n/4]$。我们证明了如果$F_i$的每个顶点都包含在多于${n-1\choose 3}-{3n/4\choose 3}$边中，那么$\{F_1, \ldots,F_{n/4}\}$允许彩虹匹配，即$n/4$边的集合由每个$F_i$的一条边组成。推广了Khan关于4-一致超图完美匹配的一个深度结果。
Let $n$ be a sufficiently large integer with $n\equiv 0\pmod 4$ and let $F_i \subseteq{[n]\choose 4}$ where $i\in [n/4]$. We show that if each vertex of $F_i$ is contained in more than ${n-1\choose 3}-{3n/4\choose 3}$ edges, then $\{F_1, \ldots ,F_{n/4}\}$ 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.