Binary matroids and local complementation

Abstract

We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic system associated with G. Moreover, a parametrized form of its Tutte polynomial yields the interlace polynomials of G.

This article supersedes arXiv:1301.0293. v2: 26 pages, 2 figures. v3 - v5: 31 pages, 2 figures v6: Final prepublication version

References in corpus (1)

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

Cited by in corpus (7)

• Matroids, Delta-matroids and Embedded Graphs
• Isotropic matroids III: Connectivity
• The transition matroid of a 4-regular graph: an introduction
• Orienting Transversals and Transition Polynomials of Multimatroids
• Isotropic matroids II: Circle graphs
• Matroids that classify forests
• The excluded 3-minors for vf-safe delta-matroids