{
  "abstract": "We prove that for every fixed $r\\geq3$, $k>0$ and $\\varepsilon\\in(0,1)$, there is $γ>0$ such that the following holds for all sufficiently large $b$. An $r$-uniform hypergraph $\\mathcal H$ whose vertex set is partitioned into parts of size at least $b$ contains at least $\\lceil(1-\\varepsilon)b\\rceil$ pairwise vertex-disjoint independent transversals, provided that the average degree in each part is at most $kb^{r-1}$ and maximum $j$-codegree $Δ_j(\\mathcal H)\\leqγb^{r-j}$ for $2\\leq j<r$. Under the same average degree, if $q$ is the minimum part size and $Δ_j(\\mathcal H)=o(q^{r-j})$ for $2\\leq j<r$, the maximum number of pairwise vertex-disjoint independent transversals is $(1-o(1))q$ as $q\\to\\infty$. We develop an iterative halving reduction for partitioned hypergraphs to apply the theorem of Delcourt and Postle on matchings avoiding forbidden submatchings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28468",
  "author_total": 2,
  "authors": [
    {
      "name": "Hanle Dai"
    },
    {
      "name": "Luyining Gan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efjd3qqaeyv8p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28468",
  "fulltext_url": null,
  "id": "efjd3qqaeyv8p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28468",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223118639",
  "pdf_url": "https://arxiv.org/pdf/2610.28468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efjd3qqaeyv8p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Independent transversals in hypergraphs with low codegrees",
  "title_text": "Independent transversals in hypergraphs with low codegrees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/efjd3qqaeyv8p",
  "venue": "arXiv",
  "versions": []
}