Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

Details Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

2007-10-23

arxiv.org/abs/0710.4266v2

Ann. Comb., 15 (2011) 675-706

Mathematics

Combinatorics

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

Scientific paper

10.1007/s00026-011-0116-3

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.

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