A new edge selection heuristic for computing the Tutte polynomial of an undirected graph

TL;DR

This paper introduces a novel edge selection heuristic that significantly improves the computation of the Tutte polynomial for large sparse graphs, demonstrated by a rapid calculation on a complex graph.

Contribution

The paper presents a new heuristic approach that enables faster computation of the Tutte polynomial for larger graphs than previously possible.

Findings

Successfully computed Tutte polynomial of the truncated icosahedron graph in under 4 minutes

Outperforms previous methods that took up to a week on multiple computers

Enables analysis of larger sparse graphs efficiently

Abstract

We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the Tutte polynomial of the truncated icosahedron graph using our Maple implementation in under 4 minutes on a single CPU. This compares with a recent result of Haggard, Pearce and Royle whose special purpose C++ software took one week on 150 computers.