A Forbidden-Minor Characterization for the Class of graphic Matroids which yield the Co-graphic Element-Splitting Matroids

TL;DR

This paper provides a precise characterization of when applying the element splitting operation to a graphic matroid results in a cographic matroid, enhancing understanding of matroid transformations.

Contribution

It offers a necessary and sufficient condition for graphic matroids to produce cographic matroids through element splitting, filling a gap in matroid theory.

Findings

Characterization of graphic matroids that yield cographic matroids after element splitting

Necessary and sufficient condition established for the operation

Improves understanding of matroid transformations and properties

Abstract

The element splitting operation on a graphic matroid, in general may not yield a cographic matroid. In this paper, we give a necessary and sufficient condition for the graphic matroid to yield cographic matroid under the element splitting operation.