{
  "annotation_id": "638665ca-ab7e-4258-9901-f90f3ea56404",
  "date_created": "2026-02-17T05:53:15.897000Z",
  "date_modified": "2026-02-17T05:53:15.897000Z",
  "file_hash": "070deaacc88251c1a63cba9b2a9efadb91a23c0ecc89e2d25834283d50503c8a",
  "private": false,
  "record": {
    "abstract": "Let $\\mathcal{H}=(V, E)$ be an $r$-uniform hypergraph on $n$ vertices. The signless Laplacian spectral radius of $\\mathcal{H}$ is defined as the maximum modulus of the eigenvalues of the tensor $\\mathcal{Q}(\\mathcal{H})=\\mathcal{D}(\\mathcal{H})+\\mathcal{A}(\\mathcal{H})$, where $\\mathcal{D}(\\mathcal{H})$ and $\\mathcal{A}(\\mathcal{H})$ are the degree diagonal tensor and the adjacency tensor of $\\mathcal{H}$, respectively. In this paper, we establish a general theorem that extends the spectral Tur\\\u0027an result of Keevash, Lenz and Mubayi [SIAM J. Discrete Math., 28 (4) (2014)]\n  to the setting of signless Laplacian spectral Tur\\\u0027an problems. We prove that if a family $\\mathcal{F}$ of $r$-uniform hypergraphs is degree-stable with respect to a family $\\mathcal{H}_n$ of $r$-uniform hypergraphs and its extremal constructions satisfy certain natural assumptions, then the signless Laplacian spectral Tur\\\u0027an problem for $\\mathcal{F}$ can be effectively reduced to the corresponding problem restricted to the family $\\mathcal{H}_n$. As a concrete application, we completely determine the extremal hypergraph that maximizes the signless Laplacian spectral radius among all Fano plane-free $3$-uniform hypergraphs, showing that the unique extremal hypergraph is the balanced complete bipartite $3$-uniform hypergraph.",
    "arxiv_id": "2601.08595",
    "authors": [
      "Yongchun Lu",
      "Jiadong Wu",
      "Liying Kang"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The signless Laplacian spectral Tur\\\u0027an problems for hypergraphs",
    "url": "https://arxiv.org/abs/2601.08595",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "26b2ea9f-80a3-4cba-8095-de9942a4c5a8",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}