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N-detachable pairs in 3-connected matroids I: Unveiling X

Brettell, Nick; Whittle, Geoff; Williams, Alan

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Authors

Nick Brettell

Geoff Whittle

Alan Williams



Abstract

Let M be a 3-connected matroid, and let N be a 3-connected minor of M. We say that a pair is N-detachable if one of the matroids or 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.

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 Article Type Article
Online Publication Date Sep 2, 2019
Publication Date Mar 31, 2020
Deposit Date Sep 18, 2019
Publicly Available Date Sep 2, 2020
Journal Journal of Combinatorial Theory, Series B
Print ISSN 0095-8956
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 141
Pages 295-342
DOI https://doi.org/10.1016/j.jctb.2019.08.005

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