Abstract
Given two undirected multigraphs G = (V, E) and H = (V, K), and two nonnegative integers l and k, we consider the problem of augmenting G and H by a smallest edge set F to obtain an l-edge-connected multigraph G + F = (V, E ∪ F) and a k-vertex-connected multigraph H + F = (V, K ∪ F). The problem includes several augmentation problems that require to increase the edge- and vertex-connectivities simultaneously. In this paper, we show that the problem with l ≥ 2 and k = 2 can be solved by adding at most one edge over the optimum in O(n4) time for two arbitrary multigraphs G and H, where n = |V|. In particular, we show that if l is even, then the problem can be solved optimally.
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