剩余为几乎2-正则的6-圈系

All Nearly 2-Regular Leaves of Partial 6-Cycle Systems

中文关键词:  完全图  6-圈系  几乎2-正则.

英文关键词:complete graph  $6$-cycle  nearly $2$-regular.

中文摘要:

      $K_{n}$为$n$阶完全图,本文研究了当完全图$K_{n}$的剩余图 $L$为几乎2-正则图时,图$K_{n}-L$的6-圈系存在的必要条件,并证明了当剩余图$L$的顶点数为$n-4$时,该必要条件也是充分条件.

英文摘要:

      Let $K_{n}$ be a complete graph on $n$ vertices. In this paper, we find the necessary conditions for the existence of a $6$-cycle system of $K_{n}-L$ for every nearly $2$-regular leave $L$ of $K_{n}$. This condition is also sufficient when the number of vertices of $L$ is $n-4$.