Kühn, Osthus, and Treglown and, independently, Khan proved that if H is a 3-uniform hypergraph with n vertices, where $n\in 3\mathbb{Z}$ and large, and ${\delta }_1(H)>\left(\begin{array}{c}n-1\\ 2\end{array}\right)-\left(\begin{array}{c}2n/3\\ 2\end{array}\right)$, then H contains a perfect matching. In this paper, we show that for $n\in 3\mathbb{Z}$ sufficiently large, if $F_1,\dots ,F_{n/3}$ are 3-uniform hypergraphs with a common vertex set and ${\delta }_1(F_i)>\left(\begin{array}{c}n-1\\ 2\end{array}\right)-\left(\begin{array}{c}2n/3\\ 2\end{array}\right)$ for $i\in [n/3]$, then $\{F_1,\dots ,F_{n/3}\}$ admits a rainbow matching, i.e., a matching consisting of one edge from each $F_i$. This is done by converting the rainbow matching problem to a perfect matching problem in a special class of uniform hypergraphs.

Kühn、Osthus 和 Treglown 以及独立的 Khan 证明了如果H是具有n个顶点的 3-均匀超图，其中$n\in 3\mathbb{Z}$ 和大，和 ${\delta }_1(H)>\left(\begin{array}{c}n-1\\ 2\end{array}\right)-\left(\begin{array}{c}2n/3\\ 2\end{array}\right)$，则H包含完美匹配。在本文中，我们证明对于$n\in 3\mathbb{Z}$ 足够大，如果 $F_1,\dots ,F_{n/3}$ 是具有公共顶点集的 3-uniform hypergraphs 和 ${\delta }_1(F_{\mathrm{一世}})>\left(\begin{array}{c}n-1\\ 2\end{array}\right)-\left(\begin{array}{c}2n/3\\ 2\end{array}\right)$ 为了 $\mathrm{一世}\in [n/3]$， 然后 $\{F_1,\dots ,F_{n/3}\}$ 承认彩虹匹配，即由每个边的一条边组成的匹配 $F_{\mathrm{一世}}$. 这是通过将彩虹匹配问题转换为一类特殊的均匀超图中的完美匹配问题来完成的。