Document Type

Article

Publication Date

11-1-2023

Abstract

Let M be an excluded minor for the class of P-representable matroids for some partial field P, let N be a 3-connected strong P-stabilizer that is non-binary, and suppose M has a pair of elements {a,b} such that M﹨a,b is 3-connected with an N-minor. Suppose also that |E(M)|≥|E(N)|+11 and M﹨a,b is not N-fragile. In the prequel to this paper, we proved that M﹨a,b is at most five elements away from an N-fragile minor. An element e in a matroid M′ is N-essential if neither M′/e nor M′﹨e has an N-minor. In this paper, we prove that, under mild assumptions, M﹨a,b is one element away from a minor having at least r(M)−2 elements that are N-essential.

Publication Source (Journal or Book title)

Journal of Combinatorial Theory Series B

First Page

272

Last Page

307

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