On the maximum size of a minimal k-edge connected augmentation

AbstractWe present a short proof of a generalization of a result of Cheriyan and Thurimella: a simple graph of minimum degree k can be augmented to a k-edge connected simple graph by adding ⩽knk+1 edges, where n is the number of nodes. One application (from the previous paper) is an approximation algorithm with a guarantee of 1+2k+1 for the following NP-hard problem: given a simple undirected graph, find a minimum-size k-edge connected spanning subgraph. For the special cases of k=4,5,6, this is the best approximation guarantee known