The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial

2006/09/01 by Sergei Chmutov, Chmutov, Sergei, Igor Pak +1
Computer Science · Mathematics · #05C10 #57M25 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0609012

openalex publication_date 2006/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Kauffman bracket [L] of a checkerboard colorable virtual link L is an evaluation of the Bollobás-Riordan polynomial R_GL 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.

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