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- W3165795633 abstract "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." @default.
- W3165795633 created "2021-06-07" @default.
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- W3165795633 date "2021-05-24" @default.
- W3165795633 modified "2023-09-26" @default.
- W3165795633 title "Obstructions for Bounded Branch-depth in Matroids" @default.
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- W3165795633 doi "https://doi.org/10.19086/aic.24227" @default.
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