{
  "abstract": "Let $H \\sim H^{k}_c(n,p)$ be an edge-colored random $k$-uniform hypergraph on the vertex set $[n]$, where each edge $e \\in \\binom{[n]}{k}$ is included independently with probability $p$ and is uniformly and independently assigned a color from the color set $[c]$. For $k = 2$, Ferber and Krivelevich (2016) established that if $c = (1+o(1))n$ and $p = (\\log n + \\log \\log n + ω(n))/n$, then with high probability the edge-colored random graph $H \\sim H^2_c(n,p)$ contains a rainbow Hamilton Berge cycle. Subsequently, Bal, Berkowitz, Devlin, and Schacht (2021) determined the threshold for the appearance of a (non-rainbow) Hamilton Berge cycle in random $k$-uniform hypergraphs. In this paper, we generalize the results to all integers $k \\ge 3$. We prove that if $c = (1+o(1))n$ and $p = (k-1)! \\frac{\\log n + \\log\\log n + ω(n)}{n^{k-1}}$, then with high probability $H \\sim H^{k}_c(n,p)$ contains a rainbow Hamilton Berge cycle. Furthermore, both conditions on $c$ and $p$ are asymptotically tight. \\noindent\\emph{Key words:} Rainbow subgraph, Hamiltonicity, Berge cycle, Random hypergraph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01989",
  "author_total": 2,
  "authors": [
    {
      "name": "Liping Zhang"
    },
    {
      "name": "Ailian Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47fznaz6dhq24.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01989",
  "fulltext_url": null,
  "id": "47fznaz6dhq24",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01989",
  "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": "W7207578512",
  "pdf_url": "https://arxiv.org/pdf/2609.01989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47fznaz6dhq24.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.01989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs",
  "title_text": "Rainbow Berge Hamiltonicity in edge-colored random k-uniform hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/47fznaz6dhq24",
  "venue": "arXiv",
  "versions": []
}