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arXiv · 1312.5401

Fan-extensions in fragile matroids

Carolyn Chun·Deborah Chun·Dillon Mayhew·Stefan H. M. van Zwam
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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.

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Carolyn Chun, Deborah Chun, Dillon Mayhew, Stefan H. M. van Zwam. 2013-12-19. Fan-extensions in fragile matroids. https://arxiv.org/abs/1312.5401

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