{
  "abstract": "We prove that every connected, locally finite, quasi-transitive graph which is quasi-isometric to a graph excluding a countable clique as a minor is quasi-isometric to a planar graph. Consequently, every finitely generated group with such a quasi-isometry is virtually planar, meaning that some finite-index subgroup admits a planar Cayley graph. We also show that a connected, locally finite, quasi-transitive graph admitting a regular map into a bounded-degree graph excluding some finite minor admits a regular map into a bounded-degree planar graph. If the source is accessible, the target need only exclude a countable clique. Combined with work of Mackay, Spriano, and the present author, this shows that a finitely presented group admits a regular map into a bounded-degree graph excluding a countable clique if and only if it is virtually planar.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12576",
  "author_total": 1,
  "authors": [
    {
      "name": "Joseph Paul MacManus"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ft7t80vfcdf5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12576",
  "fulltext_url": null,
  "id": "3ft7t80vfcdf5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12576",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.12576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ft7t80vfcdf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12576"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minor exclusion and planar rigidity",
  "title_text": "Minor exclusion and planar rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/3ft7t80vfcdf5",
  "venue": "arXiv",
  "versions": []
}