English

Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

Combinatorics 2012-03-01 v2

Abstract

We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to mutation in knot diagrams.

Keywords

Cite

@article{arxiv.0710.4266,
  title  = {Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs},
  author = {Stephen Huggett and Iain Moffatt},
  journal= {arXiv preprint arXiv:0710.4266},
  year   = {2012}
}

Comments

Version 2 has minor changes. To appear in Annals of Combinatorics