Computing the Tutte Polynomial of a Graph and the Jones Polynomial of an Alternating Link of Moderate Size

Abstract

The problem of computing the Tutte polynomial of a graph has been a hot topic in recent years, because its computation is very useful not only in graph theory but also in many problems in statistical physics, knot theory, etc. This problem is #P-hard, and there have been known only algorithms taking time at least proportional to the number of trees of a given graph which is exponential in nature. This paper presents a new algorithm by utilizing 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 in combinatorics. By this algorithm, we can compute the Tutte polynomial of any graph with at most 14 vertices and 91 edges and that of a planar graph such as 12 2 12 lattice graph with 144 vertices and 264 edges by a standard workstation in about an hour. ANY OTHER IDENTIFYING INFORMATION OF THIS REPORT DISTRIBUTION STATEMENT First issue 40 copies. This technical report is available ..