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arXiv · 2404.17306

Quickly excluding an apex-forest

Jędrzej Hodor·Hoang La·Piotr Micek·Clément Rambaud
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Abstract

We give a short proof that for every apex-forest $X$ on at least two vertices, graphs excluding $X$ as a minor have layered pathwidth at most $2|V(X)|-3$. This improves upon a result by Dujmović, Eppstein, Joret, Morin, and Wood (SIDMA, 2020). Our main tool is a structural result about graphs excluding a forest as a rooted minor, which is of independent interest. We develop similar tools for treedepth and treewidth. We discuss implications for Erdős-Pósa properties of rooted models of minors in graphs.

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Jędrzej Hodor, Hoang La, Piotr Micek, Clément Rambaud. 2025-04-04. Quickly excluding an apex-forest. https://arxiv.org/abs/2404.17306

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