{"paper":{"title":"Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Alexandr Polyanskii, Zilin Jiang","submitted_at":"2017-08-07T21:59:04Z","abstract_excerpt":"The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let $\\mathcal{F}(\\lambda)$ be the family of connected graphs of spectral radius $\\le \\lambda$. We show that $\\mathcal{F}(\\lambda)$ can be defined by a finite set of forbidden subgraphs if and only if $\\lambda < \\lambda^* := \\sqrt{2+\\sqrt{5}} \\approx 2.058$ and $\\lambda \\not\\in \\{\\alpha_2, \\alpha_3, \\dots\\}$, where $\\alpha_m = \\beta_m^{1/2} + \\beta_m^{-1/2}$ and $\\beta_m$ is the largest root of $x^{m+1}=1+x+\\dots+x^{m-1}$. The study of forbidden subgraphs characterization for $\\mathcal{F}(\\lambda)$ is motivated by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02317","kind":"arxiv","version":3},"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/1708.02317/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"}