Excluded minors are almost fragile

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Abstract

Let M be an excluded minor for the class of P-representable matroids for some partial field P, and let N be a 3-connected strong P-stabilizer that is non-binary. We prove that either M is bounded relative to N, or, up to replacing M by a Δ-Y-equivalent excluded minor, we can choose a pair of elements {a,b} such that either M\{a,b} is N-fragile, or M\{a,b} is N-fragile.

Keywords

Matroids
Excluded minors
Representations
Fragility

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The first, fourth, and fifth authors were supported by the New Zealand Marsden Fund.