Partial duality and Bollobas and Riordan's ribbon graph polynomial

Abstract

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.

References in corpus (4)

• The Jones polynomial and graphs on surfaces
• Knot invariants and the Bollobas-Riordan polynomial of embedded graphs
• Unsigned state models for the Jones polynomial
• Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

Cited by in corpus (11)

• The multivariate signed Bollobas-Riordan polynomial
• Separability and the genus of a partial dual
• Bipartite partial duals and circuits in medial graphs
• A characterization of partially dual graphs
• A Penrose polynomial for embedded graphs
• Non-orientable quasi-trees for the Bollobas-Riordan polynomial
• Partial duals of plane graphs, separability and the graphs of knots
• On a conjecture of Gross, Mansour and Tucker
• On the Seifert graphs of a link diagram and its parallels
• Arrow ribbon graphs
• A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan