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arXiv · 1212.5961

On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower

Remi C. Avohou·Joseph Ben Geloun·Etera R. Livine
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Abstract

The Bollobas-Riordan polynomial [Math. Ann. 323, 81 (2002)] extends the Tutte polynomial and its contraction/deletion rule for ordinary graphs to ribbon graphs. Given a ribbon graph $\cG$, the related polynomial should be computable from the knowledge of the terminal forms of $\cG$ namely specific induced graphs for which the contraction/deletion procedure becomes more involved. We consider some classes of terminal forms as rosette ribbon graphs with $N\ge 1$ petals and solve their associate Bollobas-Riordan polynomial. This work therefore enlarges the list of terminal forms for ribbon graphs for which the Bollobas-Riordan polynomial could be directly deduced.

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Remi C. Avohou, Joseph Ben Geloun, Etera R. Livine. 2012-12-24. On terminal forms for topological polynomials for ribbon graphs: The $N$-petal flower. https://doi.org/10.1016/j.ejc.2013.08.001

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