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Obstructions for bounded branch-depth in matroids

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Title
Obstructions for bounded branch-depth in matroids
Author(s)
J. Pascal Gollin; Kevin Hendrey; Mayhew, Dillon; Sang-il Oum
Publication Date
2021-05
Journal
Advances in Combinatorics, v.2021, no.1, pp.1 - 25
Publisher
Alliance of Diamond OA Journals
Abstract
© 2021 J. Pascal Gollin, Kevin Hendrey, Dillon Mayhew, and Sang-il Oum cb Licensed under a Creative Commons Attribution License (CC-BY).DeVos, Kwon, and Oum introduced the concept of branch-depth of matroids as a natural analogue of tree-depth of graphs. They conjectured that a matroid of sufficiently large branch-depth contains the uniform matroid Un,2n or the cycle matroid of a large fan graph as a minor. We prove that matroids with sufficiently large branch-depth either contain the cycle matroid of a large fan graph as a minor or have large branch-width. As a corollary, we prove their conjecture for matroids representable over a fixed finite field and quasi-graphic matroids, where the uniform matroid is not an option.
URI
https://pr.ibs.re.kr/handle/8788114/11032
DOI
10.19086/aic.24227
ISSN
2517-5599
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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