A Grid Theorem for Strong Immersions of Walls

ABSTRACT 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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Bibliographic Details
Published inJournal of graph theory Vol. 110; no. 1; pp. 23 - 32
Main Authors Diestel, Reinhard, Jacobs, Raphael W., Knappe, Paul, Wollan, Paul
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.09.2025
Subjects
grid theorem
strong immersion
wall
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Summary:ABSTRACT 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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ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.23245