{
  "abstract": "Let $Q$ be an $r$-graph on $q$ vertices and let $\\alpha>1$. The $(\\alpha,Q)$-spectral radius $\\lambda_{\\alpha,Q}(\\mathcal{H})$ of an $r$-graph $\\mathcal{H}$ is defined as the maximum value of the $Q$-Lagrangian polynomial over all vectors with unit $\\alpha$-norm. Given a family $\\mathcal{F}$ of $r$-graphs, the ($\\alpha, Q$)-spectral Turán number $\\operatorname{spex}_\\alpha(n, Q, \\mathcal{F})$ of $\\mathcal{F}$ is the maximum $(\\alpha,Q)$ spectral radius $\\lambda_{\\alpha, Q}(\\mathcal{H})$ among all $n$-vertex $\\mathcal{F}$-free $r$-graphs $\\mathcal{H}$. This spectral parameter provides a spectral counterpart of the generalized Turán problem and contains many classical spectral extremal problems as special cases. In this paper, we first prove that for any $\\alpha>1$ and every $2$-covered $r$-graph $Q$ with $q\\le \\ell$ vertices, the complete balanced $\\ell$-partite $r$-graph $T_{\\ell,n}^r$ uniquely maximizes $\\lambda_{\\alpha,Q}(\\mathcal{H})$ among all $n$-vertex $\\ell$-partite $r$-graphs. Based on this result and spectral stability theorems, we further determine the exact value of $\\operatorname{spex}_\\alpha(n,Q,H_F^r)$ for all sufficiently large $n$, where $H_F^r$ stands for the expansion of an edge-critical graph $F$ with chromatic number $\\ell+1$. As corollaries, we obtain several Turán-type results for graphs and $r$-graphs, including spectral bounds for the clique spectral radius of $F$-free graphs and the $\\alpha$-spectral radius of $H_{F}^r$-free $r$-graphs, where $F$ is an edge-critical graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Zijuan Cheng"
    },
    {
      "name": "Yongchun Lu"
    },
    {
      "name": "Liying Kang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zkhwnmxh5fht.bib",
  "cited_by": 0,
  "doi": "10.37236/15808",
  "fulltext_url": null,
  "id": "9zkhwnmxh5fht",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p19",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223395440",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p19/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/9zkhwnmxh5fht.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/15808",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p19"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Limits and Structures in Graph Theory",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral Generalized Turán Problems for Expansion Hypergraphs",
  "title_text": "Spectral Generalized Turán Problems for Expansion Hypergraphs",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/9zkhwnmxh5fht",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}