{"paper":{"title":"Spectral Radius Conditions for 3-Uniform Intersecting Families","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"An Chang, Guorong Gao, Lusheng Fang","submitted_at":"2026-07-09T13:26:46Z","abstract_excerpt":"Let $M_k$ denote a matching of size $k$. The classical Erd\\H{o}s matching conjecture asks for the maximum number of edges of an intersecting $r$-graph without $M_k$. The csae for $k=2$, which is known as intersecting $r$-graph, is established by Erd\\H{o}s, Ko and Rado. Hilton and Milner further determine the maximum number of edges of a non-trivial intersecting $r$-graph, where the intersecting $r$-graph $H$ is called non-trivial if $\\cap_{e\\in E(H)}e=\\emptyset$. In this paper, we investigate the spectral analogues of the hpergraph matching problems and intersecting family problems. More preci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08468","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08468/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}