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Bollobas-Riordan and relative Tutte polynomials

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.

preprint2010arXivOpen access
Clark ButlerSergei Chmutov
math.CO
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Clark ButlerSergei Chmutov

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