{"paper":{"title":"Hypergraphs with Spectral Radius at most $(r-1)!\\sqrt[r]{2+\\sqrt{5}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"Linyuan Lu, Shoudong Man","submitted_at":"2014-12-03T10:56:47Z","abstract_excerpt":"In our previous paper, we classified all $r$-uniform hypergraphs with spectral radius at most $(r-1)!\\sqrt[r]{4}$, which directly generalizes Smith's theorem for the graph case $r=2$. It is nature to ask the structures of the hypergraphs with spectral radius slightly beyond $(r-1)!\\sqrt[r]{4}$. For $r=2$, the graphs with spectral radius at most $\\sqrt{2+\\sqrt{5}}$ are classified by [{\\em Brouwer-Neumaier, Linear Algebra Appl., 1989}]. Here we consider the $r$-uniform hypergraphs $H$ with spectral radius at most $(r-1)!\\sqrt[r]{2+\\sqrt{5}}$. We show that $H$ must have a quipus-structure, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1270","kind":"arxiv","version":1},"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"}