The exact complexity of the Tutte polynomial

TL;DR

This paper surveys the computational complexity of the Tutte polynomial, providing a comprehensive overview of known results and open problems in the exact calculation of this important graph invariant.

Contribution

It consolidates and updates the state of knowledge on the exact complexity of computing the Tutte polynomial, serving as a detailed reference for researchers.

Findings

Summarizes known complexity results for Tutte polynomial computation

Identifies open problems and conjectures in the field

Provides a comprehensive overview of related topics

Abstract

This is a survey on the exact complexity of computing the Tutte polynomial. It is the longer 2017 version of Chapter 25 of the CRC Handbook on the Tutte polynomial and related topics, edited by J. Ellis-Monaghan and I. Moffatt, which is due to appear in the first quarter of 2020. In the version to be published in the Handbook the Sections 5 and 6 are shortened and made into a single section.