A grid theorem for strong immersions of walls

Paul Knappe; Paul Wollan; Raphael W. Jacobs; Reinhard Diestel

A grid theorem for strong immersions of walls

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arxiv 2301.05134 v2 pith:H26DQAGC submitted 2023-01-12 math.CO

Reinhard Diestel , Raphael W. Jacobs , Paul Knappe , Paul Wollan This is my paper · ORCID

classification math.CO

keywords graphstrongadhesionadmitcontainsdecompositiongridimmersion

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We show that a graph contains a large wall as a strong immersion minor if and only if the graph does not admit a tree-cut decomposition of small `width', which is measured in terms of its adhesion and the path-likeness of its torsos.

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Excluding a Ladder as an Induced Minor in Graphs Without Induced Stars
math.CO 2025-09 conditional novelty 7.0 of 10

Every K_{1,d}-free graph that excludes the k-ladder as an induced minor has tree-independence number bounded by a function of k and d.

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