Forbidden Minor Characterization of 3-Fold-3-Splitting of Binary Gammoid

TL;DR

This paper characterizes binary gammoids that remain binary gammoids after a 3-fold-3-point-splitting operation, providing a new approach to understanding the structural properties of these matroids.

Contribution

It introduces a novel characterization of binary gammoids under 3-fold-3-point-splitting, expanding the theoretical framework of matroid operations.

Findings

Characterization of binary gammoids preserved under 3-fold-3-point-splitting.

New approach to extend 3-fold-3-point-splitting in binary matroids.

Insight into the structural properties of binary gammoids after splitting.

Abstract

The r-fold-n-point-splitting operation is an important operation in Graph Theory defined by Slater [15]. Later, Ghafari [6] extended 3-fold-n-point-splitting operation in binary matroids and obtained the result for Eulerian matroids whose 3-fold is Eulerian. In this paper, we give another approach to extend 3-fold-3-point-splitting in binary matroids in terms of splitting and haracterize binary gammoid whose 3-fold-3-point spitting is binary gammoid.