On the Optimal Vertex-Connectivity Augmentation

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Abstract

This paper considers the problem of finding a minimum-cardinality set of edges for a given k-connected graph whose addition makes it (k + 1)-connected. We give sharp lower and upper bounds for this minimum, where the gap between them is at most k - 2. This result is a generalization of the solved cases k = 1, 2, where the exact min-max formula is known. We present a polynomial-time approximation algorithm which makes a k-connected graph (k + 1)-connected by adding a new set of edges with size at most k - 2 over the optimum.

Original languageEnglish
Pages (from-to)8-20
Number of pages13
JournalJournal of Combinatorial Theory, Series B
Volume63
Issue number1
DOIs
Publication statusPublished - Jan 1995

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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