Advertisement

On central spanning trees of a graph

  • S. Bezrukov
  • F. Kaderali
  • W. Poguntke
Graph Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1120)

Abstract

We consider the collection of all spanning trees of a graph with distance between them based on the size of the symmetric difference of their edge sets. A central spanning tree of a graph is one for which the maximal distance to all other spanning trees is minimal. We prove that the problem of constructing a central spanning tree is algorithmically difficult and leads to an NP-complete problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Amoia A., Cottafava G.: Invariance Properties of central trees, IEEE Trans. Circuit Theory, vol. CT-18 (1971), 465–467.Google Scholar
  2. [2]
    Deo D.: A central tree, IEEE Trans. Circuit Th., vol. CT-13 (1966), 439–440.Google Scholar
  3. [3]
    Garey M.R., Johnson D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman 1979.Google Scholar
  4. [4]
    Harary F.: Graph theory, Addison-Wesley Publ. Company, 1969.Google Scholar
  5. [5]
    Kaderali F.: A counterexample to the algorithm of Amoia and Cottafava for finding central trees, preprint, FB 19, TH Darmstadt, June 1973.Google Scholar
  6. [6]
    Kaderali F.: Über zentrale und maximal entfernte Bäume, unpublished manuscript.Google Scholar
  7. [7]
    Kajitani Y., Kawamoto T., Shinoda S.: A new method of circuit analysis and central trees of a graph, Electron. Commun. Japan, vol. 66 (1983), No. 1, 36–45.Google Scholar
  8. [8]
    Kawamoto T., Kajitani Y., Shinoda S.: New theorems on central trees described in connection with the principal partition of a graph, Papers of the Technical Group on Circuit and System theory of Inst. Elec. Comm. Eng. Japan, No. CST77-109 (1977), 63–69.Google Scholar
  9. [9]
    Kishi G., Kajitani Y.: Maximally distant trees and principal partition of a linear graph, IEEE Trans. Circuit Theory, vol. CT-16 (1969), 323–330.Google Scholar
  10. [10]
    Kishi G., Kajitani Y.: Maximally distant trees in a linear graph, Electronics and Communications in Japan (The Transactions of the Institute of Electronics and Communication Engineers of Japan), vol. 51 (1968), 35–42.Google Scholar
  11. [11]
    Kishi G., Kajitani Y.: On maximally distant trees, Proceedings of the Fifth Annual Allerton Conference on Circuit and System Theory, University of Illinois, Oct. 1967, 635–643.Google Scholar
  12. [12]
    Shinoda S., Kawamoto T.: On central trees of a graph, Lecture notes in Computer Sci., vol. 108 (1981), 137–151.Google Scholar
  13. [13]
    Shinoda S., Kawamoto T.: Central trees and critical sets, in Proc. 14th Asilomar Conf. on Circuit, Systems and Comp., Pacific Grove, Calif., 1980, D.E. Kirk ed., 183–187.Google Scholar
  14. [14]
    Shinoda S., Saishu K.: Conditions for an incidence set to be a central tree, Papers of the Technical Group on Circuit and System theory of Inst. Elec. Comm. Eng.Japan, No. CAS80-6 (1980), 41–46.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • S. Bezrukov
    • 1
  • F. Kaderali
    • 2
  • W. Poguntke
    • 2
  1. 1.FB Mathematik/InformatikUniversität-GH PaderbornPaderborn
  2. 2.LG KommunikationssystemeFernUniversität HagenHagen

Personalised recommendations