Prohibited Minors For Graphic Matroids That Gives A Binary Gammoid After Splitting

TL;DR

This paper characterizes specific graphic matroids that, after a splitting operation, result in binary gammoids, identifying prohibited minors that prevent this transformation.

Contribution

It provides a characterization of graphic matroids that yield binary gammoids post-splitting and identifies prohibited minors for these classes.

Findings

Identified classes of graphic matroids that produce binary gammoids after splitting.

Determined prohibited minors for graphic and cographic matroids related to binary gammoid formation.

Established conditions under which splitting preserves certain matroid properties.

Abstract

Splitting operation in Matroid Theory does not preserve graphicness, connectedness, cographicness, etc. Also, the splitting of binary gammoid does not necessarily be binary gammoid after splitting. We have characterized a class of graphic matroids that gives binary gammoids after splitting. We have obtained prohibited minors for graphic and cographic matroid which gives binary gammoid after splitting using two and three elements.