{"paper":{"title":"Spectral extremal problems for degenerate graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiadong Wu, Liying Kang, Zhenyu Ni","submitted_at":"2025-07-16T08:18:54Z","abstract_excerpt":"A family of graphs is called degenerate if it contains at least one bipartite graph. In this paper, we investigate the spectral extremal problems for a degenerate family of graphs $\\mathcal{F}$. By employing covering and independent covering of graphs, we establish a spectral stability result for $\\mathcal{F}$. Using this stability result, we prove two general theorems that characterize spectral extremal graphs for a broad class of graph families $\\mathcal{F}$ and imply several new and known results. Meanwhile, we establish the correlation between extremal graphs and spectral extremal graphs f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12014","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/2507.12014/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"}