{"paper":{"title":"Tur\\'an numbers for non-bipartite graphs and applications to spectral extremal problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Longfei Fang, Michael Tait, Mingqing Zhai","submitted_at":"2024-04-13T19:35:50Z","abstract_excerpt":"Given a graph family $\\mathcal{H}$ with $\\min_{H\\in \\mathcal{H}}\\chi(H)=r+1\\geq 3$. Let ${\\rm ex}(n,\\mathcal{H})$ and ${\\rm spex}(n,\\mathcal{H})$ be the maximum number of edges and the maximum spectral radius of the adjacency matrix over all $\\mathcal{H}$-free graphs of order $n$, respectively. Denote by ${\\rm EX}(n,\\mathcal{H})$ (resp. ${\\rm SPEX}(n,\\mathcal{H})$) the set of extremal graphs with respect to ${\\rm ex}(n,\\mathcal{H})$ (resp. ${\\rm spex}(n,\\mathcal{H})$).\n  In this paper, we use a decomposition family defined by Simonovits to give a characterization of which graph families $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09069","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/2404.09069/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"}