Abstract
We 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 ⩽ k n k + 1 edges, where n is the number of nodes. One application (from the previous paper) is an approximation algorithm with a guarantee of 1 + 2 k + 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.
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