Brettel Whittle Williams 2018 N-detachable pairs in 3-connected matroids I - Unveiling X.pdf (584.46 kB)
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N-detachable pairs in 3-connected matroids I: Unveiling X

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posted on 26.02.2020 by N Brettell, G Whittle, A Williams
© 2019 Elsevier Inc. Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair {x1,x2}⊆E(M) is N-detachable if one of the matroids M/x1/x2 or M\x1\x2 is both 3-connected and has an N-minor. This is the first in a series of three papers where we describe the structures that arise when M has no N-detachable pairs. In this paper, we prove that if no N-detachable pair can be found in M, then either M has a 3-separating set, which we call X, with certain strong structural properties, or M has one of three particular 3-separators that can appear in a matroid with no N-detachable pairs.

History

Preferred citation

Brettell, N., Whittle, G.Williams, A. (2020). N-detachable pairs in 3-connected matroids I: Unveiling X. Journal of Combinatorial Theory: Series B, 141, 295-342. https://doi.org/10.1016/j.jctb.2019.08.005

Journal title

Journal of Combinatorial Theory. Series B

Volume

141

Publication date

01/03/2020

Pagination

295-342

Publisher

Elsevier BV

Publication status

Accepted

ISSN

0095-8956

eISSN

1096-0902

Language

en

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