{
  "abstract": "Let $k\\geq 3$ and $α\\in[0,1)$, and let $λ_k(α)$ denote the $α$-spectral radius of a $k$-uniform loose cycle. Lu and Man classified all connected $k$-uniform hypergraphs with adjacency spectral radius at most $λ_k(0)$. In this paper, we extend their classification to the $α$-spectral setting. In particular, for every $k\\geq 3$ and $0<α<1$, we prove that $λ_k(α)$ is the smallest limit point of the $α$-spectral radii of connected $k$-uniform hypergraphs. Moreover, we give a complete comparison between the $α$-spectral radius of an arbitrary finite connected $k$-uniform hypergraph $H$ and that of a loose cycle by determining the sign of $ρ_α(H)-λ_k(α)$. As a consequence, for each fixed $0<α<1$, we classify all finite connected $k$-uniform hypergraphs with $α$-spectral radius at most $λ_k(α)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24024",
  "author_total": 3,
  "authors": [
    {
      "name": "Hangxi Cha"
    },
    {
      "name": "Xiaoqi Liu"
    },
    {
      "name": "Haiying Shan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akkv02f1311km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24024",
  "fulltext_url": null,
  "id": "akkv02f1311km",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24024",
  "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",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214025757",
  "pdf_url": "https://arxiv.org/pdf/2609.24024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akkv02f1311km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Uniform Hypergraphs with $α$-Spectral Radius at Most That of a Loose Cycle",
  "title_text": "Uniform Hypergraphs with α-Spectral Radius at Most That of a Loose Cycle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/akkv02f1311km",
  "venue": "arXiv",
  "versions": []
}