{
  "abstract": "Let $\\Cvec$ be a fixed orientation of the cycle $C_\\ell$, $\\ell\\ge3$, which is not directed. For an oriented graph $D$, let $d_D^*(v):=\\max\\{d_D^+(v),d_D^-(v)\\},$ and let \\[ \\sigore(D):=\\min\\bigl\\{d_D^*(x)+d_D^*(y):x\\ne y,\\ xy,yx\\notin A(D)\\bigr\\}, \\] with $\\sigore(D)=\\infty$ if the underlying graph of $D$ is complete. We prove that, for every $μ>0$, there exist $γ>0$ and $n_0$ such that every $n\\ge n_0$ with $\\ell\\mid n$ and every $n$-vertex oriented graph $D$ satisfying \\[ α(D)\\leγn \\text{ and } {\\sigore(D)\\ge\\left(\\frac34+μ\\right)n} \\] contains a $\\Cvec$-factor. {Additionally, for every fixed $s\\ge2$ and every fixed real constant $C$, we construct arbitrarily large oriented graphs with $\\sigore(D)\\ge \\frac34n+C$ that contain no $C_{2s}^{\\ad}$-factor. More precisely, $C:=\\frac34α(D)-2$ for $s=2$ and $C:=\\frac14α(D)-\\frac32$ for $s\\ge3$.} This paper develops a weighted reduction framework adapted to dominant degree condition, proves the absorption lemma via closed-cluster merging with even-walk, and derives almost-perfect tiling structures by virtue of Farkas-lemma-based fractional decomposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00889",
  "author_total": 2,
  "authors": [
    {
      "name": "Jia Zhou"
    },
    {
      "name": "Yunshu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m6ev7ywbencq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00889",
  "fulltext_url": null,
  "id": "6m6ev7ywbencq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00889",
  "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": "W7206170833",
  "pdf_url": "https://arxiv.org/pdf/2609.00889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m6ev7ywbencq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Dominant-Degree Conditions for Ramsey--Turán Factors of Non-Directed Cycle Orientations",
  "title_text": "Dominant-Degree Conditions for Ramsey--Turán Factors of Non-Directed Cycle Orientations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/6m6ev7ywbencq",
  "venue": "arXiv",
  "versions": []
}