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arXiv:0711.3490 [math.CO]AbstractReferencesReviewsResources

Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial

Sergei Chmutov

Published 2007-11-22, updated 2008-12-16Version 3

We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the Jones polynomial of links as specializations of the Bollobas-Riordan polynomials.

Comments: To appear in J. Combin. Theory Ser. B (2009), doi:10.1016/j.jctb.2008.09.007
Categories: math.CO, math.GT
Subjects: 05C10, 57M15, 57M27
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