{
  "abstract": "A thrackle is a drawing of a graph in the plane in which every pair of edges meets exactly once, either at a common endpoint or at a proper crossing. Conway conjectured that every thrackle has at most as many edges as vertices. We prove that every thrackle on $n\\ge4$ vertices has at most $\\left\\lfloor4(n-1)/3\\right\\rfloor$ edges. The proof combines Pammer's computer-assisted verification of the conjecture for graphs on at most twelve vertices with a discharging argument in suitable plane and projective-plane embeddings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31589",
  "author_total": 1,
  "authors": [
    {
      "name": "Dániel Gábor Simon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p7hgcty8ja21.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31589",
  "fulltext_url": null,
  "id": "9p7hgcty8ja21",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31589",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223293406",
  "pdf_url": "https://arxiv.org/pdf/2610.31589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p7hgcty8ja21.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31589"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Conway's thrackle conjecture: a new upper bound of $\\frac43n$",
  "title_text": "Conway's thrackle conjecture: a new upper bound of 4/3n",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/9p7hgcty8ja21",
  "venue": "arXiv",
  "versions": []
}