Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs

Fuente: arXiv
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Main Author: Distel, Marc
Format: Preprint
Published: 2025
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author Distel, Marc
author_facet Distel, Marc
contents Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every $n$-vertex $K_h$-minor-free graph has treewidth $O_h(\sqrt{n})$. Recently, Distel, Dujmović, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [SIAM J. Discrete Math. 2024] refined this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $4$ graphs. We improve this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $3$ graphs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_09063
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Distel, Marc
Combinatorics
Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every $n$-vertex $K_h$-minor-free graph has treewidth $O_h(\sqrt{n})$. Recently, Distel, Dujmović, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [SIAM J. Discrete Math. 2024] refined this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $4$ graphs. We improve this by showing that these graphs are $O_h(\sqrt{n})$-blowups of treewidth $3$ graphs.
title Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
topic Combinatorics
url https://arxiv.org/abs/2510.09063