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Improved diameter bounds for altered graphs

  • Graphs And Geometry
  • Conference paper
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Graph-Theoretic Concepts in Computer Science (WG 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 246))

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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.

The work of this author was supported by the Foundation for Computer Science (SION) of the Netherlands Organization for the Advancement of Pure Research (ZWO).

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4. References

  1. 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.

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  2. Chung, F.R.K., and M.R. Garey, Diameter bounds for altered graphs, J. Graph Theory 8 (1984) 511–534.

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  3. Ghouila-Houri, A., Un résultat relatif á la notion de diamètre, C.R. Acad. Sci. de Paris 250 (1960) 4254–4256.

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  4. Plesnik, J., Note on diametrically critical graphs, Recent Advances in Graph Theory, Proc. 2nd Czechoslovak Symp. (Prague 1974), Academia, Prague (1975) 455–465.

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

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Utrecht, P.O.Box 80.012, 3508 TA, Utrecht, the Netherlands

    A. A. Schoone, H. L. Bodlaender & J. van Leeuwen

Authors
  1. A. A. Schoone
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  2. H. L. Bodlaender
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  3. J. van Leeuwen
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Editor information

Gottfried Tinhofer Gunther Schmidt

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© 1987 Springer-Verlag Berlin Heidelberg

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Schoone, A.A., Bodlaender, H.L., van Leeuwen, J. (1987). Improved diameter bounds for altered graphs. In: Tinhofer, G., Schmidt, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1986. Lecture Notes in Computer Science, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17218-1_61

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  • DOI: https://doi.org/10.1007/3-540-17218-1_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17218-5

  • Online ISBN: 978-3-540-47415-9

  • eBook Packages: Springer Book Archive

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