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.