Negami's like splitting formula for the Jones polynomial

TL;DR

This paper develops a new splitting formula inspired by Negami's for the Jones polynomial, addressing limitations in applying existing formulas to non-planar graph contractions, and introduces a novel splitting matrix.

Contribution

The authors construct a new splitting formula for the Jones polynomial that works for non-planar graph contractions, extending Negami's original approach.

Findings

New splitting formula for Jones polynomial

Splitting matrix differs from Lindström matrix

Potential for further generalizations

Abstract

Negami's splitting formula cannot be directly applied to get a Jones polynomial splitting formula for the contraction of certain planar graphs in the decomposition become non planar. Therefore, we build a Negami's like splitting formula from the scratch. Now, the new splitting matrix doesn't have the form of a Lindstr\"om matrix and it would be interesting to have similar results for it.