Bollobas-Riordan and relative Tutte polynomials
Combinatorics
2010-11-02 v1
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.
Keywords
Cite
@article{arxiv.1011.0072,
title = {Bollobas-Riordan and relative Tutte polynomials},
author = {Clark Butler and Sergei Chmutov},
journal= {arXiv preprint arXiv:1011.0072},
year = {2010}
}
Comments
10 pages, many figures