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Quickly excluding an apex-forest

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arxiv 2404.17306 v2 pith:TUSKARBD submitted 2024-04-26 math.CO cs.DM

Jędrzej Hodor , Hoang La , Piotr Micek , Clément Rambaud This is my paper · ORCID
classification math.COcs.DM
keywords excludinggraphsapex-forestminorresultrooteddevelopdiscuss
verification ladder T0 review T1 audit T2 compute T3 formal
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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 Dujmovi\'c, 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 Erd\H{o}s-P\'osa properties of rooted models of minors in graphs.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Excluding a rectangular grid

    math.CO 2025-01 conditional novelty 8.0 of 10

    A new parameter family, k-treedepth, is characterized by excluded minors T□P_l for all k-vertex trees T, unifying treedepth, the ladder theorem, and the Grid-Minor Theorem.

  2. Erd\H{o}s-P\'osa property of rooted tree minors

    math.CO 2026-07 accept novelty 7.0 of 10

    Rooted tree minors satisfy a linear Erdős-Pósa bound: k vertex-disjoint rooted models or a hitting set of O(k) vertices.

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