Characterizing matroids whose bases form graphic delta-matroids

TL;DR

This paper introduces delta-graphic matroids, characterizes their structure, and identifies that all forbidden minors have at most 48 elements, expanding understanding of matroid classes related to graph theory.

Contribution

It provides a structural characterization of delta-graphic matroids and bounds the size of their forbidden minors, linking graphic and cographic matroids within regular matroids.

Findings

Delta-graphic matroids include graphic and cographic matroids.

Forbidden minors for delta-graphic matroids have at most 48 elements.

The class of delta-graphic matroids is a proper subclass of regular matroids.

Abstract

We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass of the class of regular matroids. We give a structural characterization of the class of delta-graphic matroids. We also show that every forbidden minor for the class of delta-graphic matroids has at most $48$ elements.