{
  "abstract": "Let $C(n)$ denote the maximum number of directed Hamiltonian cycles in a tournament on $n$ vertices. We prove that, as $n\\to\\infty$, $$ C(n) = \\left(\\frac{\\cosh 1}{\\cos 1}\\pm o(1)\\right)\\frac{(n-1)!}{2^n}. $$ The bound is asymptotically attained by the regular tournament with vertices $\\mathbb Z/n\\mathbb Z$ where $(i,j)$ is a directed edge if $j - i \\pmod n< n/2$. This answers a question of Alon and proves a conjecture of Wormald. Among the other implications of these results is asymptotically determining the maximum number of Hamiltonian paths in a tournament on $n$ vertices. We provide our own exposition of these proofs, which were originally found by GPT-5.6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23755",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Divoux"
    },
    {
      "name": "Shouda Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23z1esf70vy6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23755",
  "fulltext_url": null,
  "id": "23z1esf70vy6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23755",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7222976589",
  "pdf_url": "https://arxiv.org/pdf/2610.23755",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23z1esf70vy6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23755",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23755"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The maximum number of Hamiltonian cycles in tournaments",
  "title_text": "The maximum number of Hamiltonian cycles in tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/23z1esf70vy6s",
  "venue": "arXiv",
  "versions": []
}