Session 7A

Algorithms and Computations

Volume 1004 of the series Lecture Notes in Computer Science pp 224-233

Date:

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 #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.