{
  "id": "1812.06032",
  "version": "v1",
  "published": "2018-12-14T17:12:58.000Z",
  "updated": "2018-12-14T17:12:58.000Z",
  "title": "The extremal $p$-spectral radius of Berge-hypergraphs",
  "authors": [
    "Liying Kang",
    "Lele Liu",
    "Linyuan Lu",
    "Zhiyu Wang"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph. We say that a hypergraph $H$ is a Berge-$G$ if there is a bijection $\\phi: E(G)\\to E(H)$ such that $e\\subseteq \\phi(e)$ for all $e\\in E(G)$. For any $r$-uniform hypergraph $H$ and a real number $p\\geq 1$, the $p$-spectral radius $\\lambda^{(p)}(H)$ of $H$ is defined as \\[ \\lambda^{(p)}(H):=\\max_{{\\bf x}\\in\\mathbb{R}^n,\\,\\|{\\bf x}\\|_p=1} r\\sum_{\\{i_1,i_2,\\ldots,i_r\\}\\in E(H)} x_{i_1}x_{i_2}\\cdots x_{i_r}. \\] In this paper, we study the $p$-spectral radius of Berge-$G$ hypergraphs. We determine the $3$-uniform hypergraphs with maximum $p$-spectral radius for $p\\geq 1$ among Berge-$G$ hypergraphs when $G$ is a path, a cycle or a star.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-14T17:12:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "15A18"
    ],
    "keywords": [
      "spectral radius",
      "berge-hypergraphs",
      "uniform hypergraph",
      "real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}