论文标题
Erdős-ko-Rado定理，以$ 2 $的改造家庭，有完美的匹配家庭
The Erdős-Ko-Rado theorem for $2$-intersecting families of perfect matchings
论文作者
论文摘要
$ 2K $顶点的完整图表中的完美匹配是一组边缘，使得没有两个边缘具有一个共同的顶点，并且每个顶点都完全涵盖一次。据说两个完美的匹配是$ t $ - 如果它们至少有$ t $边缘的共同点。本文的主要结果是将著名的Erdős-Ko-Rado（EKR）定理\ cite {ekr}扩展到两个相互匹配的家庭，以适合所有$ K $的完美匹配。具体来说，对于$ k \ geq 3 $，一组2间交流的完美匹配，$ k_ {2k} $的最大尺寸的$（2k-5）（2k-5）（2k-7）（2k-7）\ cdots（1）$ $完美匹配。
A perfect matching in the complete graph on $2k$ vertices is a set of edges such that no two edges have a vertex in common and every vertex is covered exactly once. Two perfect matchings are said to be $t$-intersecting if they have at least $t$ edges in common. The main result in this paper is an extension of the famous Erdős-Ko-Rado (EKR) theorem \cite{EKR} to 2-intersecting families of perfect matchings for all values of $k$. Specifically, for $k\geq 3$ a set of 2-intersecting perfect matchings in $K_{2k}$ of maximum size has $(2k-5)(2k-7)\cdots (1)$ perfect matchings.
