Abstract
Given a k-vertex-connected directed graph G, what is the minimum number m, such that G can be made k+1-connected by the addition of m new edges? We prove that if a vertex v has in- and out-degree at least k+1, there exists a splittable pair of edges on v. With the help of this statement, we generalize the basic result of Eswaran and Tarjan, and give lower and upper bounds for m which are equal for k=0 and differ from each other by at most k otherwise. Furthermore, a polynomial approximation algorithm is given for finding an almost optimal augmenting set.
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© 1993 Springer-Verlag Berlin Heidelberg
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Jordán, T. (1993). Increasing the vertex-connectivity in directed graphs. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_59
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DOI: https://doi.org/10.1007/3-540-57273-2_59
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