Note on the treewidth of graphs excluding a disjoint union of cycles as a minor
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918324468711424 |
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| author | Joret, Gwenaël Micek, Piotr |
| author_facet | Joret, Gwenaël Micek, Piotr |
| contents | For a planar graph $H$, let $f(H)$ denote the minimum integer such that all graphs excluding $H$ as a minor have treewidth at most $f(H)$. We show that if $H$ is a disjoint union of $k$ cycles then $f(H)=O(|V(H)| + k \log k)$, which is best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05844 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note on the treewidth of graphs excluding a disjoint union of cycles as a minor Joret, Gwenaël Micek, Piotr Combinatorics Discrete Mathematics For a planar graph $H$, let $f(H)$ denote the minimum integer such that all graphs excluding $H$ as a minor have treewidth at most $f(H)$. We show that if $H$ is a disjoint union of $k$ cycles then $f(H)=O(|V(H)| + k \log k)$, which is best possible. |
| title | Note on the treewidth of graphs excluding a disjoint union of cycles as a minor |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2602.05844 |