Geodesic
Obstructions for bounded branch-depth in matroids
Advances in Combinatronics (2021)

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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 Combinatronics},
     publisher = {mathdoc},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a5/}
}
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%A Dillon Mayhew
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%F ADVC_2021_a5
J. Pascal Gollin; Kevin Hendrey; Dillon Mayhew; Sang-il Oum. Obstructions for bounded branch-depth in matroids. Advances in Combinatronics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a5/