{
  "abstract": "Jackson and Thomassen conjectured that every $2k$-strong digraph contains a spanning $k$-strong oriented subdigraph. We prove sharp degree conditions for the existence of such a subdigraph. For every fixed positive integer $k$ and all sufficiently large $n$, every $n$-vertex digraph $D$ with $δ^0(D)\\ge\\lfloor(n+k-1)/2\\rfloor$ admits a $k$-strong orientation. This threshold is best possible even for the weaker conclusion that $D$ itself is $k$-strong. We also prove a sharp Woodall-type analogue for every fixed positive integer $k$ and all sufficiently large $n$: if $d_D^+(x)+d_D^-(y)\\ge n+2k-2$ for every missing arc $xy$, then $D$ admits a $k$-strong orientation, and this bound is again best possible. As a further consequence, we determine the sharp minimum total degree threshold. Finally, the semi-degree result also remains valid when $k\\leαn$ for every fixed $0<α<0.094882\\ldots$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36551",
  "author_total": 2,
  "authors": [
    {
      "name": "Jørgen Bang-Jensen"
    },
    {
      "name": "Shuo Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehqeadbsxfarg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36551",
  "fulltext_url": null,
  "id": "ehqeadbsxfarg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36551",
  "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": "W7214923737",
  "pdf_url": "https://arxiv.org/pdf/2609.36551",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehqeadbsxfarg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36551",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36551"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Degree conditions for $k$-strong orientations of digraphs",
  "title_text": "Degree conditions for k-strong orientations of digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/ehqeadbsxfarg",
  "venue": "arXiv",
  "versions": []
}