{
  "abstract": "Hadwiger's conjecture (1943) states that every graph $G$ with chromatic number at least $t$ contains a $K_t$-model: a collection of $t$ vertex-disjoint connected subgraphs $T_1,\\dots,T_t$ such that for all $1\\le i<j\\le t$ some vertex in $T_j$ has a neighbour in $T_i$. Replacing \"some\" in this definition by \"every\" gives rise to the significantly stronger notion of a dominating $K_t$-model introduced by Illingworth and Wood (2024). They raised the question whether every graph of chromatic number at least $t$ contains a dominating $K_t$-model. This statement is a significant strengthening of Hadwiger's conjecture and has come to be known as the dominating Hadwiger conjecture. We provide our own exposition of a disproof of this conjecture found by ChatGPT 6 Astra Ultra. The construction is the complement of a pseudorandom triangle-free graph that is obtained by randomly subsampling a block geometric graph based on the Suzuki-Tits ovoid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35361",
  "author_total": 2,
  "authors": [
    {
      "name": "Freddie Illingworth"
    },
    {
      "name": "Raphael Steiner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5d19mpke75z99.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35361",
  "fulltext_url": null,
  "id": "5d19mpke75z99",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35361",
  "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": "W7214781091",
  "pdf_url": "https://arxiv.org/pdf/2609.35361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5d19mpke75z99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Disproof of the dominating Hadwiger conjecture",
  "title_text": "Disproof of the dominating Hadwiger conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5d19mpke75z99",
  "venue": "arXiv",
  "versions": []
}