{
  "abstract": "We prove that for every integer $d\\ge2$ and all sufficiently large $m$, every digraph with $m$ edges and minimum outdegree at least $d$ has a vertex bipartition for which each directed cut is of size at least \\[\\left\\lceil\\frac{d-1}{2(2d-1)}m+\\frac{d^2}{2(2d-1)}\\right\\rceil.\\] The bound is sharp for infinitely many $m$. This answers for large graphs a question of Scott and proves a conjecture of Lee, Loh, and Sudakov. For $d=2$ we prove that $\\lceil m/6\\rceil$ is achievable for all $m$. We also establish a stability result characterizing near-extremal graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21381",
  "author_total": 2,
  "authors": [
    {
      "name": "Frederic Folz"
    },
    {
      "name": "Mykhaylo Tyomkyn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ebghc9mybxf62.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21381",
  "fulltext_url": null,
  "id": "ebghc9mybxf62",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21381",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.21381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ebghc9mybxf62.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21381"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Optimally large cuts in both directions",
  "title_text": "Optimally large cuts in both directions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/ebghc9mybxf62",
  "venue": "arXiv",
  "versions": []
}