{
  "abstract": "The linear list Hadwiger conjecture asserts that every $K_t$-minor-free graph is $O(t)$-choosable. Following an approach outlined by Delcourt and Postle, we recently established $O(t\\log\\log t)$-choosability. Soon afterward, OpenAI provided a proof of the conjecture. A key new ingredient of their proof is a linear bound on the choice number of $K_t$-minor-free graphs with at most $t^{11/10}$ vertices. In this paper, we give a relatively simple proof of this small-graph bound for graphs with at most $t(\\ln t)^5$ vertices.Combining this with the argument from our earlier $O(t\\log\\log t)$ bound, we obtain a shorter and somewhat more accessible proof of the conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01946",
  "author_total": 2,
  "authors": [
    {
      "name": "Yangyan Gu"
    },
    {
      "name": "Rongxing Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c25zhfwmzq3ym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01946",
  "fulltext_url": null,
  "id": "c25zhfwmzq3ym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01946",
  "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"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7216493245",
  "pdf_url": "https://arxiv.org/pdf/2610.01946",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c25zhfwmzq3ym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.01946",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01946"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A shorter proof of the linear list Hadwiger conjecture",
  "title_text": "A shorter proof of the linear list Hadwiger conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/c25zhfwmzq3ym",
  "venue": "arXiv",
  "versions": []
}