Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width

Abstract

It is known that evaluating the Tutte polynomial, $T(G; x, y)$, of a graph, $G$, is $\#$P-hard at all but eight specific points and one specific curve of the $(x, y)$-plane. In contrast we show that if $k$ is a fixed constant then for graphs of tree-width at most $k$ there is an algorithm that will evaluate the polynomial at any point using only a linear number of multiplications and additions.