{"paper":{"title":"The extremal $p$-spectral radius of Berge-hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lele Liu, Linyuan Lu, Liying Kang, Zhiyu Wang","submitted_at":"2018-12-14T17:12:58Z","abstract_excerpt":"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 Be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06032","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}