If $\mathcal{S}$ is a set of matroids, then the matroid $M$ is $\mathcal{S}$-fragile if, for every element $e\in E(M)$, either $M\backslash e$ or $M/e$ has no minor isomorphic to a member of $\mathcal{S}$. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when $\mathcal{M}$ is a minor-closed class of $\mathcal{S}$-fragile matroids, and $N\in \mathcal{M}$, the only members of $\mathcal{M}$ that contain $N$ as a minor are obtained from $N$ by increasing the length of fans. We prove that if this is the case, then we can certify it with a finite case-analysis. The analysis involves examining matroids that are at most two elements larger than $N$.
@article{10_37236_3994,
author = {Carolyn Chun and Deborah Chun and Dillon Mayhew and Stefan H. M. Van Zwam},
title = {Fan-extensions in fragile matroids},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/3994},
zbl = {1328.05035},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3994/}
}
TY - JOUR
AU - Carolyn Chun
AU - Deborah Chun
AU - Dillon Mayhew
AU - Stefan H. M. Van Zwam
TI - Fan-extensions in fragile matroids
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3994/
DO - 10.37236/3994
ID - 10_37236_3994
ER -
%0 Journal Article
%A Carolyn Chun
%A Deborah Chun
%A Dillon Mayhew
%A Stefan H. M. Van Zwam
%T Fan-extensions in fragile matroids
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3994/
%R 10.37236/3994
%F 10_37236_3994
Carolyn Chun; Deborah Chun; Dillon Mayhew; Stefan H. M. Van Zwam. Fan-extensions in fragile matroids. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/3994
