Elementary Lift and Single Element Coextension of A Binary Gammoid

TL;DR

This paper investigates the conditions under which elementary lift and single element coextension operations preserve the binary gammoid property by identifying forbidden minors.

Contribution

It identifies forbidden minors for binary gammoids that are not preserved under elementary lift and coextension operations.

Findings

Forbidden minors for elementary lift preserving binary gammoids.

Forbidden minors for single element coextensions preserving binary gammoids.

Conditions under which these operations maintain the binary gammoid property.

Abstract

Elementary lift is a generalized splitting operation. Splitting of a binary gammoid need not be a gammoid. This paper finds forbidden minors for a binary gammoid whose elementary lift is a binary gammoid. We also find forbidden minors for a binary gammoid whose single element coextension is a binary gammoid.