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arXiv · 2003.13975

Obstructions for bounded branch-depth in matroids

J. Pascal Gollin·Kevin Hendrey·Dillon Mayhew·Sang-il Oum
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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 $U_{n,2n}$ 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.

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J. Pascal Gollin, Kevin Hendrey, Dillon Mayhew, Sang-il Oum. 2020-03-31. Obstructions for bounded branch-depth in matroids. https://doi.org/10.19086/aic.24227

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