{
  "abstract": "An $r$-uniform hypergraph is linear if any two edges share at most one vertex. For a family $\\mathcal F$ of $r$-graphs, let $\\text{ex}^{\\text{lin}}_r(n,\\mathcal F)$ and $\\text{spex}^{\\text{lin}}_r(n,\\mathcal F)$ denote, respectively, the maximum number of edges and the maximum spectral radius of an $n$-vertex $\\mathcal F$-free linear $r$-graph. In this paper, we show that for $t\\ge s\\ge3$, $\\text{spex}^{\\text{lin}}_r(n,K_{s,t}^{+})\\le \\frac{(t-s+1)^{1/s}}{r-1}n^{1-1/s}+o(n^{1-1/s})$, where $K_{s,t}^{+}$ is the $r$-graph obtained from the complete bipartite graph $K_{s,t}$ by enlarging each edge with $r-2$ new vertices. This answers a problem of She, Fan and Kang in a stronger form. Moreover, our result implies that $\\text{ex}^\\text{lin}_r(n,K_{s,t}^{+}) \\le \\frac{(t-s+1)^{1/s}}{r(r-1)}n^{2-1/s}+o(n^{2-1/s})$, which improves the leading coefficient in the corresponding bound of Gao and Chang. We also give a construction which implies that $\\text{spex}^{\\text{lin}}_r(n,K_{s,t}^{+})=Θ(n^{1-1/s})$ and $\\text{ex}^\\text{lin}_r(n,K_{s,t}^{+})=Θ(n^{2-1/s})$ for $s\\ge 4r-6$ and $t>(s-1)!$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34065",
  "author_total": 2,
  "authors": [
    {
      "name": "Lusheng Fang"
    },
    {
      "name": "Guorong Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tg68g96zyt3s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34065",
  "fulltext_url": null,
  "id": "8tg68g96zyt3s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34065",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223845827",
  "pdf_url": "https://arxiv.org/pdf/2610.34065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tg68g96zyt3s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral Turán problems for complete bipartite expansions in linear hypergraphs",
  "title_text": "Spectral Turán problems for complete bipartite expansions in linear hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8tg68g96zyt3s",
  "venue": "arXiv",
  "versions": []
}