Fan-extensions in fragile matroids
Abstract
If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when F is a minor-closed class of S-fragile matroids, and N is in F, the only members of F 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2013
- DOI:
- 10.48550/arXiv.1312.5401
- arXiv:
- arXiv:1312.5401
- Bibcode:
- 2013arXiv1312.5401C
- Keywords:
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- Mathematics - Combinatorics;
- 05B35
- E-Print:
- Small revisions and corrections