{
  "abstract": "A loose hypertree is a hypergraph whose incidence graph is a tree. Let $b\\ge3$, $n\\equiv1\\pmod{b-1}$, and $s:=(n-1)/(b-1)$. We determine the largest $t$-intersecting families of loose spanning $b$-uniform hypertrees on $[n]$, simultaneously for every $1\\le t\\le s$, provided $n$ exceeds an explicit constant depending only on $b$. The extremal families consist of all such hypertrees containing a fixed $t$-edge loose forest whose component sizes are as equal as the divisibility condition permits. In particular, when $bt\\le n$, the extremal forests are matchings. We also prove a Hilton--Milner-type bound: if $n\\ge C_b(t+1)$, where $C_b$ depends only on $b$, every nontrivial $t$-intersecting family has at most $(s+1)r_{t+1}(n)$ members. Here $r_j(n)$ is the maximum possible number of loose spanning $b$-uniform hypertrees containing a fixed $j$-edge loose forest. For fixed constants $b,t$, this bound is asymptotically sharp and is $O_{b,t}(n^{2-b})r_t(n)$. The proofs combine exact forest enumeration with the intersection theorems of Kupavskii for spread families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20443",
  "author_total": 2,
  "authors": [
    {
      "name": "Yury Person"
    },
    {
      "name": "Thomas Schweser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1htt668vwcrgc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20443",
  "fulltext_url": null,
  "id": "1htt668vwcrgc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20443",
  "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": "W7222276136",
  "pdf_url": "https://arxiv.org/pdf/2610.20443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1htt668vwcrgc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Intersecting families of loose spanning hypertrees",
  "title_text": "Intersecting families of loose spanning hypertrees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1htt668vwcrgc",
  "venue": "arXiv",
  "versions": []
}