The minimum augmentation of any graph to a K‐edge‐connected graph

For a graph G₀ = (V, E₀) and an integer K, how many edges are needed for augmenting G₀ to a K‐edge‐connected graph? Results in the literature have answered this in several special cases such as when G₀ is a tree, or when K = 2. In this paper, we settle the problem in the general case where G₀ can be any multigraph and K can be any positive integer. We obtained both good characterization and good algorithm for the problem. Applications of our algorithm are suggested in designing a reliable network aiming at the most effective use of exising network.