All Nearly 2-Regular Leaves of Partial 6-Cycle Systems
Received:August 28, 2012  Revised:May 17, 2013
Key Words: complete graph   $6$-cycle   nearly $2$-regular.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071163).
Author NameAffiliation
Liqun PU School of Mathematics and Statistics, Zhengzhou University, Henan 450001, P. R. China 
Hengzhou XU School of Mathematics and Statistics, Zhengzhou University, Henan 450001, P. R. China 
Hao SHEN Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China 
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Abstract:
      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 $n-4$.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.06.002
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