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arXiv · 2602.05844

Note on the treewidth of graphs excluding a disjoint union of cycles as a minor

Gwenaël Joret·Piotr Micek
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Abstract

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.

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Gwenaël Joret, Piotr Micek. 2026-02-05. Note on the treewidth of graphs excluding a disjoint union of cycles as a minor. https://arxiv.org/abs/2602.05844

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