Volume 1004 of the series Lecture Notes in Computer Science pp 224233
Computing the Tutte polynomial of a graph of moderate size
 Kyoko SekineAffiliated withDepartment of Information Science, University of Tokyo
 , Hiroshi ImaiAffiliated withDepartment of Information Science, University of Tokyo
 , Seiichiro TaniAffiliated withNippon Telegraph and Telephone Corporation
Abstract
The problem of computing the Tutte polynomial of a graph is #Phard in general, and any known algorithm takes exponential time at least. This paper presents a new algorithm by exploiting a fact that many 2isomorphic 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.
 Title
 Computing the Tutte polynomial of a graph of moderate size
 Book Title
 Algorithms and Computations
 Book Subtitle
 6th International Symposium, ISAAC '95 Cairns, Australia, December 4–6, 1995 Proceedings
 Pages
 pp 224233
 Copyright
 1995
 DOI
 10.1007/BFb0015427
 Print ISBN
 9783540605737
 Online ISBN
 9783540477662
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1004
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Kyoko Sekine ^{(1)}
 Hiroshi Imai ^{(1)}
 Seiichiro Tani ^{(2)}
 Author Affiliations

 1. Department of Information Science, University of Tokyo, Japan
 2. Nippon Telegraph and Telephone Corporation, Japan
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