论文标题
3-均匀超图的彩虹匹配
Rainbow matchings for 3-uniform hypergraphs
论文作者
论文摘要
Kühn，Osthus和Treglown，独立的Khan证明，如果$ h $是$ 3 $均匀的超图，则具有$ n $ dertices，以便$ n $ dertices，以便$ n \ in 3 \ mathbb {z} $ and gigal，并且$δ_1（h）> {h）> {n-1 \ oplect 2} - n-1 \ oplect 2} - complete coption coption coption $ contsion copters $ and copt $ n $ and $ han $ and $ n $在本文中，我们表明$ n \ in 3 \ mathbb {z} $足够大，如果$ f_1，\ ldots，f_ {n/3} $是3-均匀的hypergrapghs，具有通用顶点套装，并且$Δ_1（f_i）> {n-1 \ in 2} - {2} - {2n/3]然后，$ \ {f_1，\ dots，f_ {n/3} \} $允许彩虹匹配，即，每个$ f_i $中的一个边缘组成的匹配。这是通过将彩虹匹配的问题转换为特殊类别统一超图中的完美匹配问题来完成的。
Kühn, Osthus, and Treglown and, independently, Khan proved that if $H$ is a $3$-uniform hypergraph with $n$ vertices such that $n\in 3\mathbb{Z}$ and large, and $δ_1(H)>{n-1\choose 2}-{2n/3\choose 2}$, then $H$ contains a perfect matching. In this paper, we show that for $n\in 3\mathbb{Z}$ sufficiently large, if $F_1, \ldots, F_{n/3}$ are 3-uniform hypergrapghs with a common vertex set and $δ_1(F_i)>{n-1\choose 2}-{2n/3\choose 2}$ 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.
