{
  "abstract": "The first major step in the theory of graph minors of Robertson and Seymour was the grid theorem, a fundamental duality result describing that any graph of sufficiently high treewidth must contain a large grid as a minor. Since this pioneering work, multiple grid theorems have been established in structural graph theory, linking various width parameters of combinatorial objects with the non-existence of grid-like obstructions. In particular, Kawarabayashi and Kreutzer [STOC'15] proved a variant of the grid theorem for directed graphs that links directed treewidth with the non-existence of topological minors of large cylindrical walls. On the other hand, to study immersions of undirected graphs $-$ another containment relation that focuses on edge-disjointness, rather than vertex-disjointness $-$ Wollan [JCTB'15] introduced a parameter, tree-cutwidth, and proved that it is dual to immersions of large walls. In this work, we present a version of Wollan's parameter for directed graphs, the directed tree-cutwidth. The main result is a grid theorem for directed tree-cutwidth, establishing that it is dual to directed immersions of large cylindrical walls.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20391",
  "author_total": 4,
  "authors": [
    {
      "name": "Marcin Briański"
    },
    {
      "name": "Meike Hatzel"
    },
    {
      "name": "Karolina Okrasa"
    },
    {
      "name": "Michał Pilipczuk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43497jdyvjzd8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20391",
  "fulltext_url": null,
  "id": "43497jdyvjzd8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20391",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221938488",
  "pdf_url": "https://arxiv.org/pdf/2610.20391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43497jdyvjzd8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Potatoes and Onions",
  "title_text": "Potatoes and Onions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/43497jdyvjzd8",
  "venue": "arXiv",
  "versions": []
}