{
  "abstract": "Let $k\\ge2$ be a fixed integer. Bollobás and Scott proved that every $3$-uniform hypergraph with $m$ edges admits a partition of its vertex set into $k$ parts such that each part spans at most $m/k^3+O_k(m^{6/7})$ edges. Scott later suggested that the error term should be $O_k(m^{2/3})$. In this paper, we show that every $3$-uniform hypergraph with $m$ edges admits a partition into $k$ parts such that each part spans at most $m/k^3+O_k(m^{2/3})$ edges, thereby establishing the proposed error term.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09864",
  "author_total": 2,
  "authors": [
    {
      "name": "Siwei Lin"
    },
    {
      "name": "Qinghou Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xpa5jbhnefq4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09864",
  "fulltext_url": null,
  "id": "6xpa5jbhnefq4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09864",
  "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": "W7220911058",
  "pdf_url": "https://arxiv.org/pdf/2610.09864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xpa5jbhnefq4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The $O(m^{2/3})$ error term for judicious partitions of 3-uniform hypergraphs",
  "title_text": "The O(m^2/3) error term for judicious partitions of 3-uniform hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/6xpa5jbhnefq4",
  "venue": "arXiv",
  "versions": []
}