English

A grid theorem for strong immersions of walls

Combinatorics 2025-01-22 v2

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.

Keywords

Cite

@article{arxiv.2301.05134,
  title  = {A grid theorem for strong immersions of walls},
  author = {Reinhard Diestel and Raphael W. Jacobs and Paul Knappe and Paul Wollan},
  journal= {arXiv preprint arXiv:2301.05134},
  year   = {2025}
}

Comments

16 pages, corrected indices in Lemma 3.1, minor changes compared to previous version