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Improved diameter bounds for altered graphs

  • A. A. Schoone
  • H. L. Bodlaender
  • J. van Leeuwen
Graphs And Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 246)

Abstract

We consider the following problem: Given positive integers k and D, what is the maximum diameter of the graph obtained by deleting k edges from a graph G with diameter D, assuming that the resulting graph is still connected. For undirected graphs G we prove an upper bound of (k+1)D and a lower bound of (k+1)D-k for even D and of (k+1)D-2k+2 for odd D≥3. For directed graphs G, the bounds depend strongly on D: for D=1 and D=2 we derive exact bounds of θ (√k) and of 2k+2, respectively, while for D≥3 the resulting diameter is in general unbounded in terms of k and D.

Keywords

Short Path Directed Graph Maximum Diameter Undirected Graph Diameter Increase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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4. References

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    Schoone, A.A., H.L. Bodlaender and J. van Leeuwen, Diameter increase caused by edge deletion, J. of Graph Theory, (to appear).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • A. A. Schoone
    • 1
  • H. L. Bodlaender
    • 1
  • J. van Leeuwen
    • 1
  1. 1.Department of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands

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