Abstract
In this chapter we discuss the important problem of increasing the (arc)-strong connectivity of a given directed (multi)graph by a number of different operations. These include adding new arcs, reversing existing arcs and deorienting arcs. In Section 14.1 we introduce the operation of splitting off a pair of arcs incident with a vertex. We prove Mader’s splitting theorem which allows one to give inductive proofs for several important results on directed multigraphs. In Section 14.2, using Mader’s theorem, we describe a solution, due to Frank, for the problem of finding a minimum cardinality set of new arcs to add to a directed multigraph such that the result is a k-arc-strong directed multigraph. In Section 14.3 we describe a solution by Frank and Jordán of the analogous problem for vertex-strong connectivity.
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© 2009 Springer-Verlag London Limited
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Bang-Jensen, J., Gutin, G.Z. (2009). Increasing Connectivity. In: Digraphs. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-84800-998-1_14
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DOI: https://doi.org/10.1007/978-1-84800-998-1_14
Publisher Name: Springer, London
Print ISBN: 978-0-85729-041-0
Online ISBN: 978-1-84800-998-1
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