The contractible subgraph of 5-connected graphs |
| |
Authors: | Chengfu Qin Xiaofeng Guo Weihua Yang |
| |
Institution: | 1. School of Mathematics Science, Guangxi Teachers Education University, 530001, Nanning, Guangxi, P.R.China 2. School of Mathematics Science, Xiamen University, 310065, Xiamen, Fujian, P.R.China 3. Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, P.R.China
|
| |
Abstract: | An edge e of a k-connected graph G is said to be k-removable if G — e is still k-connected. A subgraph H of a k-connected graph is said to be k-contractible if its contraction results still in a k-connected graph. A k-connected graph with neither removable edge nor contractible subgraph is said to be minor minimally k-connected. In this paper, we show that there is a contractible subgraph in a 5-connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex of minor minimally 5-connected graph is contained in some triangle. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|