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.

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.