This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minor-closed. Also, we prove that finite-rank minors of gammoids are gammoids. Furthermore, the topological gammoids of Carmesin (2014) are proved to coincide, as matroids, with the finitary gammoids. A corollary is that topological gammoids are minor-closed.It is a well-known fact that the dual of any finite strict gammoid is a transversal matroid. The class of strict gammoids defined by digraphs not containing alternating combs, introduced in Afzali Borujeni et. al. (2015), contains examples which are not dual to any transversal matroid. However, we describe the duals of matroids in this class as a natural extension of transversal matroids. While finite gammoids are closed under duality, we construct a strict gammoid that is not dual to any gammoid.
@article{10_37236_5107,
author = {Seyed Hadi Afzali Borujeni and Hiu-Fai Law and Malte M\"uller},
title = {Infinite gammoids: minors and duality},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5107},
zbl = {1329.05057},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5107/}
}
TY - JOUR
AU - Seyed Hadi Afzali Borujeni
AU - Hiu-Fai Law
AU - Malte Müller
TI - Infinite gammoids: minors and duality
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5107/
DO - 10.37236/5107
ID - 10_37236_5107
ER -
%0 Journal Article
%A Seyed Hadi Afzali Borujeni
%A Hiu-Fai Law
%A Malte Müller
%T Infinite gammoids: minors and duality
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5107/
%R 10.37236/5107
%F 10_37236_5107
Seyed Hadi Afzali Borujeni; Hiu-Fai Law; Malte Müller. Infinite gammoids: minors and duality. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5107
