Expansions for the Bollobás-Riordan Polynomial of Separable Ribbon Graphs
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We define 2-decompositions of ribbon graphs, which generalize 2-sums and tensor products of graphs. We give formulae for the Bollobás-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.
Mathematics Subject Classification05C31 05C10 57M15
Keywordsribbon graph embedded graph 2-sum tensor product Tutte polynomial Bollobás-Riordan polynomial Ribbon graph polynomial Jones polynomial
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