A 2-isomorphism theorem for delta-matroids

TL;DR

This paper extends Whitney's 2-Isomorphism Theorem to graphs embedded in surfaces, providing a characterization for when such graphs have isomorphic delta-matroids, thus generalizing classical graph-matroid relationships.

Contribution

It introduces a novel 2-isomorphism theorem for delta-matroids associated with surface-embedded graphs, expanding the understanding of graph-matroid correspondences.

Findings

Characterization of when two surface-embedded graphs have isomorphic delta-matroids

Extension of classical 2-Isomorphism Theorem to delta-matroids in surface graphs

Framework for analyzing graph isomorphisms via delta-matroids in topological settings

Abstract

Whitney's 2-Isomorphism Theorem characterises when two graphs have isomorphic cycle matroids. We present an analogue of this theorem for graphs embedded in surfaces by characterising when two graphs in surface have isomorphic delta-matroids.