# The structure of delta-matroids with width one twists

## TL;DR

This paper characterizes delta-matroids with a twist of width one, providing a structural theorem and an excluded minor characterization to better understand their properties and classifications.

## Contribution

It introduces a Rough Structure Theorem for delta-matroids with width-one twists and offers an excluded minor characterization for such delta-matroids.

## Key findings

- Structural theorem for delta-matroids with width-one twists
- Excluded minor characterization of these delta-matroids
- Enhanced understanding of delta-matroid classifications

## Abstract

The width of a delta-matroid is the difference in size between a maximal and minimal feasible set. We give a Rough Structure Theorem for delta-matroids that admit a twist of width one. We apply this theorem to give an excluded minor characterisation of delta-matroids that admit a twist of width at most one.