Partial duality and Bollobas and Riordan's ribbon graph polynomial

Details Partial duality and Bollobas and Riordan's ribbon graph polynomial Partial duality and Bollobas and Riordan's ribbon graph polynomial

2008-09-17

arxiv.org/abs/0809.3014v2

Discrete Math., 310 (2010) 174-183

Mathematics

Combinatorics

Scientific paper

10.1016/j.disc.2009.08.008

Recently S. Chmutov introduced a generalization of the dual of a ribbon (or embedded) graph and proved a relation between Bollobas and Riordan's ribbon graph polynomial of a ribbon graph and its generalized duals. Here I show that the duality relation satisfied by the ribbon graph polynomial can be understood in terms of knot theory and I give a simple proof of the relation via the homfly polynomial of a knot.

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