Connectivity keeping edges in graphs with large minimum degree |
| |
Authors: | Shinya Fujita Ken-ichi Kawarabayashi |
| |
Institution: | aDepartment of Mathematics, Gunma National College of Technology, Toribamachi 580, Maebashi, Gunma 371-8530, Japan;bNational Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan |
| |
Abstract: | The old well-known result of Chartrand, Kaugars and Lick says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G−v is still k-connected. In this paper, we consider a generalization of the above result G. Chartrand, A. Kaigars, D.R. Lick, Critically n-connected graphs, Proc. Amer. Math. Soc. 32 (1972) 63–68]. We prove the following result:Suppose G is a k-connected graph with minimum degree at least 3k/2+2. Then G has an edge e such that G−V(e) is still k-connected.The bound on the minimum degree is essentially best possible. |
| |
Keywords: | Connectivity Minimum degree Edge deletion |
本文献已被 ScienceDirect 等数据库收录! |
|