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)


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.


Short Path Directed Graph Maximum Diameter Undirected Graph Diameter Increase 
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4. References

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    Chung, F.R.K., Diameters of communication networks, in: M. Anshel and W. Gewirtz (eds.), Mathematics of information processing, Proc. Symposia in Applied Math., vol 34, American Math. Soc., Providence, RI, 1986, pp. 1–18.Google Scholar
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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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