The transition matroid of a 4-regular graph: an introduction

preprint2015arXivOpen access

Given a 4-regular graph $F$ , we introduce a binary matroid $M_τ(F)$ on the set of transitions of $F$ . Parametrized versions of the Tutte polynomial of $M_τ(F)$ yield several well-known graph and knot polynomials, including the Martin polynomial, the homflypt polynomial, the Kauffman polynomial and the Bollobás-Riordan polynomial.

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The transition matroid of a 4-regular graph: an introduction

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