Matroid fragility and relaxations of circuit hyperplanes

We relate two conjectures that play a central role in the reported proof of Rota's Conjecture. Let F be a finite field. The first conjecture states that: the branch-width of any F-representable N-fragile matroid is bounded by a function depending only upon F and N. The second conjecture states...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series B 2020-05, Vol.142, p.36-42
Main Authors: Geelen, Jim, Hoersch, Florian
Format: Article
Language:English
Subjects:
Circuit-hyperplane relaxation
Matroid fragility
Rota's Conjecture
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Summary:We relate two conjectures that play a central role in the reported proof of Rota's Conjecture. Let F be a finite field. The first conjecture states that: the branch-width of any F-representable N-fragile matroid is bounded by a function depending only upon F and N. The second conjecture states that: if a matroid M2 is obtained from a matroid M1 by relaxing a circuit-hyperplane and both M1 and M2 are F-representable, then the branch-width of M1 is bounded by a function depending only upon F. Our main result is that the second conjecture implies the first.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2019.08.007