{
  "abstract": "Let $r\\ge2$, let $T_r$ denote the transitive tournament on $r$ vertices, and write $d_G^*(v):=\\max\\{d_G^+(v),d_G^-(v)\\}$. We prove that if $r\\mid n$ and an $n$-vertex digraph $G$ satisfies $d_G^*(x)+d_G^*(y)\\ge 2(1-1/r)n-1$ for every $x\\ne y \\in V(G)$ with $xy \\notin E(G)$, then $G$ has a $T_r$-factor, and the bound is best possible. Furthermore, by applying our main theorem, we settle Treglown's conjecture on the dominant degree $d^*_G(x) \\ge (1-1/r)n$ and answer Molla and Treglown's problem of determining the exact Ore-type threshold $2(1-1/r)n - 1$, and we obtain stronger versions of the theorems of Czygrinow, DeBiasio, Kierstead and Molla.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.10445",
  "author_total": 3,
  "authors": [
    {
      "name": "Yufei Chang"
    },
    {
      "name": "Shuo Wei"
    },
    {
      "name": "Jin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7kdw6eewka236.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.10445",
  "fulltext_url": null,
  "id": "7kdw6eewka236",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.10445",
  "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": "W7202270081",
  "pdf_url": "https://arxiv.org/pdf/2608.10445",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7kdw6eewka236.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2608.10445",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.10445"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Exact Dominant Degree Condition for Transitive Tournament Factors in Digraphs",
  "title_text": "An Exact Dominant Degree Condition for Transitive Tournament Factors in Digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/7kdw6eewka236",
  "venue": "arXiv",
  "versions": []
}