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

Abstract

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

v1: 29 pages, 9 figures. v2: minor corrections. v3: 30 pages, 9 figures. v4: 31 pages, 11 figures. v5: 34 pages, 11 figures v6: 42 pages, 19 figures . The definition of balanced mutation is corrected, and the discussion of touch-graphs is expanded. v7: 43 pages, 19 figures. Further changes may be made before publication in the European Journal of Combinatorics

References in corpus (1)

• Binary matroids and local complementation

Cited by in corpus (2)

• Binary matroids and local complementation
• Transition polynomial as a weight system for binary delta-matroids