Computing the Tutte polynomial of a graph of moderate size

  • Kyoko Sekine
  • Hiroshi Imai
  • Seiichiro Tani
Session 7A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1004)


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 Berlin Heidelberg 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

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