Geodesic
Obstructions for bounded branch-depth in matroids
Advances in Combinatorics (2021) Cet article a éte moissonné depuis la source Scholastica

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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 $U_{n,2n}$ 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.
Publié le : 
@article{ADVC_2021_a5,
     author = {J. Pascal Gollin and Kevin Hendrey and Dillon Mayhew and Sang-il Oum},
     title = {Obstructions for bounded branch-depth in matroids},
     journal = {Advances in Combinatorics},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a5/}
}
TY  - JOUR
AU  - J. Pascal Gollin
AU  - Kevin Hendrey
AU  - Dillon Mayhew
AU  - Sang-il Oum
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JO  - Advances in Combinatorics
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/ADVC_2021_a5/
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%0 Journal Article
%A J. Pascal Gollin
%A Kevin Hendrey
%A Dillon Mayhew
%A Sang-il Oum
%T Obstructions for bounded branch-depth in matroids
%J Advances in Combinatorics
%D 2021
%U http://geodesic.mathdoc.fr/item/ADVC_2021_a5/
%G en
%F ADVC_2021_a5
J. Pascal Gollin; Kevin Hendrey; Dillon Mayhew; Sang-il Oum. Obstructions for bounded branch-depth in matroids. Advances in Combinatorics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a5/