Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions for bounded branch-depth in matroids   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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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn