Arrow ribbon graphs

Abstract

We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollobás-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect to the partial duality of ribbon graphs. We construct an arrow ribbon graph from a virtual link whose extended Bollobás-Riordan polynomial specializes to the arrow polynomial of the virtual link recently introduced by H.Dye and L.Kauffman. This result generalizes the classical Thistlethwaite theorem to the arrow polynomial of virtual links.

to appear in Journal of Knot Theory and Its Ramifications

References in corpus (6)

• The Jones polynomial and graphs on surfaces
• The multivariate signed Bollobas-Riordan polynomial
• Knot invariants and the Bollobas-Riordan polynomial of embedded graphs
• Twisted duality for embedded graphs
• Partial duality and Bollobas and Riordan's ribbon graph polynomial
• A characterization of partially dual graphs

Cited by in corpus (1)

• On a conjecture of Gross, Mansour and Tucker