Duality Respecting Representations and Compatible Complexity Measures for Gammoids
Combinatorics
2022-06-07 v2
Abstract
We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.
Cite
@article{arxiv.1807.00588,
title = {Duality Respecting Representations and Compatible Complexity Measures for Gammoids},
author = {Immanuel Albrecht},
journal= {arXiv preprint arXiv:1807.00588},
year = {2022}
}