{
  "abstract": "The Erdős--Gallai theorem determines the maximum number of edges in a graph with bounded matching number; its clique-counting extension replaces edges by $s$-cliques, and a spectral analogue in terms of the $s$-clique tensor has recently been established. We study the corresponding $\\mathcal A_α$-tensor of the $s$-uniform clique hypergraph. For $0\\leqα\\leq1$ and $3\\le s\\le2t-1$, we determine the maximum $α$-$s$-clique spectral radius among $n$-vertex graphs containing no matching of $t$ edges: when $3\\le s\\le t$ and $n$ is sufficiently large, the maximum is attained by the join of a clique of order $t-1$ and an independent set, and when $t<s\\le 2t-1$ and $n\\ge2t-1$, it is attained by a clique of order $2t-1$ together with isolated vertices. At $α=0$, these statements recover the known result for the $s$-clique spectral radius; at $α=1$, they yield the corresponding statement for the maximum $s$-clique degree. For $s=t\\ge3$, we obtain the maximum for every $n\\ge2t-1$; at $α=0$, this removes the requirement that $n$ be sufficiently large from the known result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08605",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaoqi Liu"
    },
    {
      "name": "Haiying Shan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yvm8ps7hm4n4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08605",
  "fulltext_url": null,
  "id": "5yvm8ps7hm4n4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08605",
  "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": "W7220956226",
  "pdf_url": "https://arxiv.org/pdf/2610.08605",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yvm8ps7hm4n4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08605",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08605"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spectral Erdős--Gallai Theorems for the \\(\\mathcal A_α\\)-Tensor of the \\(s\\)-Clique Hypergraph",
  "title_text": "Spectral Erdős--Gallai Theorems for the 𝒜_α-Tensor of the s-Clique Hypergraph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5yvm8ps7hm4n4",
  "venue": "arXiv",
  "versions": []
}