# On the HOMFLY and Tutte polynomials

## TL;DR

This paper explores the relationship between the HOMFLY polynomial of knots and the Tutte polynomial of associated plane graphs, showing that the HOMFLY polynomial can be determined from Tutte polynomials.

## Contribution

It establishes that the HOMFLY polynomial of a knot is determined by the Tutte polynomials of associated plane graphs, addressing the converse of a known result.

## Key findings

- HOMFLY polynomial is determined by Tutte polynomials of associated graphs
- Addresses the inverse relationship of Jaeger's result
- Provides a method to derive HOMFLY from Tutte polynomials

## Abstract

A celebrated result of F. Jaeger states that the Tutte polynomial of a planar graph is determined by the HOMFLY polynomial of an associated link. Here we are interested in the converse of this result. We consider the question `to what extent does the Tutte polynomial determine the HOMFLY polynomial of any knot?' We show that the HOMFLY polynomial of a knot is determined by Tutte polynomials of plane graphs associated to the knot.

---
Source: https://tomesphere.com/paper/0704.0644