The Kauffman bracket of virtual links and the Bollob\'as-Riordan polynomial

By Sergei Chmutov, Igor Pak. 2006

59 citations recorded by the source corpus.

We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollob\'as-Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes Thistlethwaite's celebrated theorem relating the Kauffman bracket with the Tutte polynomial of planar graphs.

Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9e963d23e1b8f106a8171f75275c534cae90b9dc

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In Computer Graphics and Computer-Aided Design

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt

In Discrete Mathematics and Combinatorics

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt

In Geometry and Topology

1. Joanna A. Ellis-Monaghan
2. Iain Moffatt

Citations in the corpus

• Twisted duality for embedded graphs (2009, methodology): “The signed Bollobás-Riordan polynomial was introduced by Chmutov and Pak in [21] to extend some relations between the topological Tutte polynomial and the Jones polynomial of a virtual link, and then Vignes-Tourneret [86] provided a multivariate generalization of the signed Bollobás-Riordan polynomi”