{
  "abstract": "Norin and Steiner recently proved the Linear Hadwiger Conjecture. That is, there is an absolute constant $C$ such that every graph $G$ satisfies $χ(G)\\leqslant C\\,\\text{had}(G)$, where $χ(G)$ is the chromatic number and $\\text{had}(G)$ is the Hadwiger number of $G$. They estimate that their proof gives a non-optimised constant $C$ of order $10^{100}$. This paper uses AI assistance to optimise their argument, and shows that every graph $G$ satisfies $χ(G)\\,\\leqslant\\,1{,}118{,}430\\,\\text{had}(G)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10831",
  "author_total": 1,
  "authors": [
    {
      "name": "David R. Wood"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nh9vse8f2r6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10831",
  "fulltext_url": null,
  "id": "2nh9vse8f2r6g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10831",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221148525",
  "pdf_url": "https://arxiv.org/pdf/2610.10831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nh9vse8f2r6g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.10831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tweaking the constant in the Linear Hadwiger Theorem",
  "title_text": "Tweaking the constant in the Linear Hadwiger Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/2nh9vse8f2r6g",
  "venue": "arXiv",
  "versions": []
}