Bollobas-Riordan and relative Tutte polynomials

2010/10/30 by Butler, Clark, Chmutov, Sergei
#05C10 #05C31 #57M15 #57M25 #57M27 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1011.0072

Abstract

We establish a relation between the Bollobas-Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its projection to the plane in a nontrivial way. Also we give a duality formula for the relative Tutte polynomial of dual plane graphs and an expression of the Kauffman bracket of a virtual link as a specialization of the relative Tutte polynomial.

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