Obstructions for Bounded Branch-depth in Matroids

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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. © 2021 J. Pascal Gollin, Kevin Hendrey, Dillon Mayhew, and Sang-il Oum cb Licensed under a Creative Commons Attribution License (CC-BY).
Publisher
Alliance of Diamond Open Access Journals
Issue Date
2021-05
Language
English
Article Type
Article
Citation

Advances in Combinatorics, v.2021, no.1, pp.1 - 25

ISSN
2517-5599
DOI
10.19086/aic.24227
URI
http://hdl.handle.net/10203/287238
Appears in Collection
MA-Journal Papers(저널논문)
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