Extremal graphs in connectivity augmentation

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2 Citations (Scopus)

Abstract

Let A(n, k, t) denote the smallest integer e for which every k-connected graph on n vertices can be made (k + t)-connected by adding e new edges. We determine A(n, k, t) for all values of n, k, and t in the case of (directed and undirected) edge-connectivity and also for directed vertex-connectivity. For undirected vertex-connectivity we determine A(n, k, 1) for all values of n and k. We also describe the graphs that attain the extremal values.

Original languageEnglish
Pages (from-to)179-193
Number of pages15
JournalJournal of Graph Theory
Volume31
Issue number3
DOIs
Publication statusPublished - Jul 1999

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Keywords

  • Connectivity
  • Directed graphs
  • Edge-splitting
  • Graph connectivity augmentation

ASJC Scopus subject areas

  • Geometry and Topology

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