Connectivity keeping edges in graphs with large minimum degree

The old well-known result of Chartrand, Kaugars and Lick [1] 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. 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. Key Words Connectivity, minimum degree, edge deletion.

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Shinya Fujita, Ken-ichi Kawarabayashi
• Keywords: JCT 2008, K-connected Graph, Minimum Degree, Paper