Heavy Arc Orientations of Gammoids

TL;DR

This paper presents a new combinatorial method to derive realizable orientations of gammoids directly from a total order on their digraph's arcs, bypassing the need for matrix representations over the reals.

Contribution

It introduces a purely combinatorial approach to obtain realizable orientations of gammoids from arc orderings, simplifying previous matrix-based methods.

Findings

Provides a new combinatorial technique for gammoid orientations

Eliminates the need for matrix representations over reals

Enables direct derivation of realizable orientations from arc orderings

Abstract

In this work, we introduce a purely combinatorial way to obtain realizable orientations of a gammoid from a total order on the arc set of the digraph representing it, without first obtaining a matrix representing the gammoid over the reals.