Brylawski and Seymour independently proved that if $M$ is a connected matroid with a connected minor $N$, and $e \in E(M) - E(N)$, then $M \backslash e$ or $M / e$ is connected having $N$ as a minor. This paper proves an analogous but somewhat weaker result for $2$-polymatroids. Specifically, if $M$ is a connected $2$-polymatroid with a proper connected minor $N$, then there is an element $e$ of $E(M) - E(N)$ such that $M \backslash e$ or $M / e$ is connected having $N$ as a minor. We also consider what can be said about the uniqueness of the way in which the elements of $E(M) - E(N)$ can be removed so that connectedness is always maintained.
@article{10_37236_8369,
author = {Zachary Gershkoff and James Oxley},
title = {A note on the connectivity of 2-polymatroid minors},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8369},
zbl = {1427.05046},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8369/}
}
TY - JOUR
AU - Zachary Gershkoff
AU - James Oxley
TI - A note on the connectivity of 2-polymatroid minors
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8369/
DO - 10.37236/8369
ID - 10_37236_8369
ER -
%0 Journal Article
%A Zachary Gershkoff
%A James Oxley
%T A note on the connectivity of 2-polymatroid minors
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8369/
%R 10.37236/8369
%F 10_37236_8369
Zachary Gershkoff; James Oxley. A note on the connectivity of 2-polymatroid minors. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8369
