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

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