{
  "abstract": "For a tournament $T$ and a vertex ordering $\\prec$, let $T^{\\prec}$ be the graph of backward arcs in $\\prec$. The diclique number of a tournament is $\\domega(T)=\\min_{\\prec}ω(T^{\\prec})$, and the dichromatic number is $\\dchi(T)=\\min_{\\prec}χ(T^{\\prec})$. We prove a mixed parameter transfer theorem: for all $k$ and $r$, if $\\tww(T)\\le k$ and $ω(T^{\\prec})\\le r$, then the ordered twin-width of $(T^{\\prec},\\prec)$ is bounded by a function of $k$ and $r$. The proof combines the regular-semigrid theorem for ordered graphs with permutation-encoding obstructions to bounded twin-width in tournaments. Together with polynomial $χ$-boundedness of graphs of bounded twin-width, this implies that tournaments of bounded twin-width are $\\dchi$-bounded by $\\domega$, resolving a conjecture of Aboulker, Aubian, Charbit, and Lopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02763",
  "author_total": 2,
  "authors": [
    {
      "name": "Chaoliang Tang"
    },
    {
      "name": "Junchi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99m8gwtvm5ctt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02763",
  "fulltext_url": null,
  "id": "99m8gwtvm5ctt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02763",
  "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": "W7207522471",
  "pdf_url": "https://arxiv.org/pdf/2609.02763",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99m8gwtvm5ctt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02763",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02763"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bounded Twin-Width Tournaments are $\\dchi$-Bounded",
  "title_text": "Bounded Twin-Width Tournaments are dchi-Bounded",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/99m8gwtvm5ctt",
  "venue": "arXiv",
  "versions": []
}