Extremal graphs in connectivity augmentation

  • Authors:

  • Tibor Jordán

  • Affiliations:

  • Department of Mathematics and Computer Science, Odense University, Campusvej 55, DK-5230, Odense, Denmark

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 1999

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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. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 179–193, 1999