{"paper":{"title":"Spectral extremal results on edge blow-up of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huiqiu Lin, Longfei Fang","submitted_at":"2023-10-08T09:19:32Z","abstract_excerpt":"Let ${\\rm ex}(n,F)$ and ${\\rm spex}(n,F)$ be the maximum size and maximum spectral radius of an $F$-free graph of order $n$, respectively. The value ${\\rm spex}(n,F)$ is called the spectral extremal value of $F$. Nikiforov [J. Graph Theory 62 (2009) 362--368] gave the spectral Stability Lemma, which implies that for every $\\varepsilon>0$, sufficiently large $n$ and a non-bipartite graph $H$ with chromatic number $\\chi(H)$, the extremal graph for ${\\rm spex}(n,H)$ can be obtained from the Tur\\'{a}n graph $T_{\\chi(H)-1}(n)$ by adding and deleting at most $\\varepsilon n^2$ edges. It is still a ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05085","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/2310.05085/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"}