{
  "abstract": "We prove a degree-sequence resilience theorem for Hamilton Berge cycles in random uniform hypergraphs. For every fixed integer $k\\ge3$ and every $γ>0$, there exists $C=C(k,γ)>0$ such that if $C\\log n/n^{k-1}\\le p\\le1$, then asymptotically almost surely every spanning subhypergraph of $H^{(k)}(n,p)$ with increasing vertex-degree sequence $g_1\\le\\cdots\\le g_n$ satisfying \\[ g_i\\ge\\left(\\left(\\frac{i}{n}\\right)^{k-1}+γ\\right) \\binom{n-1}{k-1}p \\qquad(1\\le i<n/2) \\] contains a Hamilton Berge cycle. The term $(i/n)^{k-1}$ agrees with the normalized asymptotic degree bound in Salia's deterministic Pósa-type theorem. Our result gives a hypergraph analogue of the random-graph theorem of Condon et al. and strengthens the sharp Dirac-type resilience theorem of Chen and Zhang at the same logarithmic probability order. The deletion-resilience formulation has optimal probability order up to constant factors. The coefficient $1$ of $(i/n)^{k-1}$ cannot be replaced by a smaller constant. The proof controls adaptive rotations and representative-edge incidences uniformly. It also gives an endpoint-growth estimate under nonuniform deletion bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08525",
  "author_total": 3,
  "authors": [
    {
      "name": "Liping Zhang"
    },
    {
      "name": "Ailian Chen"
    },
    {
      "name": "Qinghai Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ax7qrpbraaqtm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08525",
  "fulltext_url": null,
  "id": "ax7qrpbraaqtm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08525",
  "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/2611.08525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ax7qrpbraaqtm.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Pósa-type resilience for Hamilton Berge cycles in random hypergraphs",
  "title_text": "Pósa-type resilience for Hamilton Berge cycles in random hypergraphs",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/ax7qrpbraaqtm",
  "venue": "arXiv",
  "versions": []
}