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

Brettell, Nick; Whittle, Geoff; Williams, Alan

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
• Public URL: https://durham-repository.worktribe.com/output/1291416