Computing the Tutte polynomial of a graph of moderate size

  • Kyoko Sekine
  • Hiroshi Imai
  • Seiichiro Tani
Session 7A

DOI: 10.1007/BFb0015427

Volume 1004 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Sekine K., Imai H., Tani S. (1995) Computing the Tutte polynomial of a graph of moderate size. In: Staples J., Eades P., Katoh N., Moffat A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg

Abstract

The problem of computing the Tutte polynomial of a graph is #P-hard in general, and any known algorithm takes exponential time at least. This paper presents a new algorithm by exploiting a fact that many 2-isomorphic minors appear in the process of computation. The complexity of the algorithm is analyzed in terms of Bell numbers and Catalan numbers. This algorithm enables us to compute practically the Tutte polynomial of any graph with at most 14 vertices and 91 edges, and that of a planar graph such as 12×12 lattice graph with 144 vertices and 264 edges.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Kyoko Sekine
    • 1
  • Hiroshi Imai
    • 1
  • Seiichiro Tani
    • 2
  1. 1.Department of Information ScienceUniversity of TokyoJapan
  2. 2.Nippon Telegraph and Telephone CorporationJapan