Fan-Extensions in Fragile Matroids

• DOI: 10.37236/3994
• Publication Date: 2020-01-10T23:59:24Z
• Authors: Carolyn Chun; Deborah Chun; Dillon Mayhew; Stefan H. M. Van ...
• Keywords: Minor (academic); Backslash

If $\mathcal{S}$ is a set of matroids, then the matroid $M$ $\mathcal{S}$-fragile if, for every element $e\in E(M)$, either $M\backslash e$ or $M/e$ has no minor isomorphic to member $\mathcal{S}$. Excluded-minor characterizations often depend, implicitly explicitly, on understanding classes fragile matroids. In certain cases, when $\mathcal{M}$ minor-closed class and $N\in \mathcal{M}$, only members that contain $N$ as are obtained from by increasing length fans. We prove if this case, we can certify it with finite case-analysis. The analysis involves examining matroids at most two elements larger than $N$.