{"paper":{"title":"Extensions on spectral extrema of $C_5/C_6$-free graphs with given size","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuchao Li, Wanting Sun, Wei Wei","submitted_at":"2022-06-18T23:11:45Z","abstract_excerpt":"Let $\\mathcal{F}$ denote a set of graphs. A graph $G$ is said to be $\\mathcal{F}$-free if it does not contain any element of $\\mathcal{F}$ as a subgraph. The Tur\\'an number is the maximum possible number of edges in an $\\mathcal{F}$-free graph with $n$ vertices. It is well known that classical Tur\\'an type extremal problem aims to study the Tur\\'an number of fixed graphs. In 2010, Nikiforov \\cite{Nik2} proposed analogously a spectral Tur\\'an type problem which asks to determine the maximum spectral radius of an $\\mathcal{F}$-free graph with $n$ vertices. It attracts much attention and many suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.09295","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.09295/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"}