Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915543607410688 |
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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 |