{
  "abstract": "Let $r\\ge 3$ and $k\\ge 2r+1$ be fixed integers. We determine, for all sufficiently large $n$, the maximum adjacency-tensor spectral radius of an $n$-vertex $r$-uniform hypergraph containing no Berge cycle of length at least $k$. Write $s=\\left\\lfloor\\frac{k-1}{2}\\right\\rfloor$. If $k=2s+1$ is odd, the unique extremal hypergraph consists of all $r$-sets containing at most one vertex outside a fixed $s$-set. If $k=2s+2$ is even, one additionally includes all $r$-sets containing a fixed pair outside the $s$-set together with $r-2$ vertices inside it. Consequently, the maximum spectral radius is given as \\[ \\operatorname{spex}_r(n,k) = \\left[ \\binom{s}{r-1} \\left(\\frac{r-1}{s}\\right)^{(r-1)/r} +o(1) \\right]n^{(r-1)/r}. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25030",
  "author_total": 3,
  "authors": [
    {
      "name": "Lihua Feng"
    },
    {
      "name": "Lu Lu"
    },
    {
      "name": "Tingzeng Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26v5jmqpcbbc0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25030",
  "fulltext_url": null,
  "id": "26v5jmqpcbbc0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25030",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214095493",
  "pdf_url": "https://arxiv.org/pdf/2609.25030",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26v5jmqpcbbc0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25030",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25030"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral extremal hypergraphs without long Berge cycles",
  "title_text": "Spectral extremal hypergraphs without long Berge cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/26v5jmqpcbbc0",
  "venue": "arXiv",
  "versions": []
}