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arXiv · 2212.12371

Deletion-Contraction and the Surface Tutte Polynomial

Iain Moffatt·Maya Thompson
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Abstract

In this paper we unify two families of topological Tutte polynomials. The first family is that coming from the surface Tutte polynomial, a polynomial that arises in the theory of local flows and tensions. The second family arises from the canonical Tutte polynomials of Hopf algebras. Each family includes the Las Vergnas, Bollobás-Riordan, and Krushkal polynomials. As a consequence we determine a deletion-contraction definition of the surface Tutte polynomial and recursion relations for the number of local flows and tensions in an embedded graph.

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Iain Moffatt, Maya Thompson. 2024-01-25. Deletion-Contraction and the Surface Tutte Polynomial. https://arxiv.org/abs/2212.12371

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