Canonical binary $\Delta$-matroids

TL;DR

This paper extends the canonical form theory for binary delta-matroids, removing previous restrictions on the empty set's feasibility, and generalizes handle slide operations from ribbon graphs to delta-matroids.

Contribution

It introduces a canonical form for binary delta-matroids without restrictions on the empty set, broadening the scope of previous work on handle slide operations.

Findings

Established a canonical form for all binary delta-matroids

Generalized handle slide operations to delta-matroids

Removed feasibility restrictions on the empty set

Abstract

The handle slide operation, originally defined for ribbon graphs, was extended to delta-matroids by I. Moffatt and E. Mphako-Bandab, who show that, using a delta-matroid analogue of handle slides, every binary delta-matroid in which the empty set is feasible can be written in a canonical form analogous to the canonical form for one-vertex maps on a surface. We provide a canonical form for binary delta-matroids without restriction on the feasibility of the empty set.