2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210585We 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.To appear in J. Combin. Theory Ser. B (2009), doi:10.1016/j.jctb.2008.09.007CombinatoricsGeometric Topology05C10; 57M15; 57M27text