We prove that, for any finite field, nets provide a qualitative characterization for branch-width in the class of representable matroids.
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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 ...
Dec 20, 2005 · For matroids representable over a given finite field, we obtain a qualitative characterization of large branch-width. For graphs, such a ...
We prove that, for any finite field F, nets provide a qualitative characterization for branch-width in the class of F-representable matroids.
Geelen, J. F., Gerards, A. M. H., Robertson, N., & Whittle, G. (2003). Obstructions to branch-decomposition of matroids. (School of Mathematical and Computing ...
Geelen, J., Gerards, B., Robertson, N., & Whittle, G. (2006). Obstructions to branch-decomposition of matroids. Journal of Combinatorial Theory - Series B, ...
May 24, 2021 · The branch-depth of a matroid M is defined to be the minimum integer k for which M admits a. (k,k)-decomposition if E(M) has more than one ...
The branch-depth of a matroid M is defined to be the minimum integer k for which M admits a pk, kq-decomposition if EpMq has more than one element, and is ...
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Oct 22, 2024 · We prove that, for any finite field F, nets provide a qualitative characterization for branch-width in the class of F-representable matroids.