English

Partial duality and Bollobas and Riordan's ribbon graph polynomial

Combinatorics 2012-03-01 v2

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.

Keywords

Cite

@article{arxiv.0809.3014,
  title  = {Partial duality and Bollobas and Riordan's ribbon graph polynomial},
  author = {Iain Moffatt},
  journal= {arXiv preprint arXiv:0809.3014},
  year   = {2012}
}
R2 v1 2026-06-21T11:21:19.861Z