{"paper":{"title":"A precise threshold for quasi-Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guus Regts, J\\'anos Pach, Ross J. Kang, Viresh Patel","submitted_at":"2014-03-14T00:21:32Z","abstract_excerpt":"We consider a variation of Ramsey numbers introduced by Erd\\H{o}s and Pach (1983), where instead of seeking complete or independent sets we only seek a $t$-homogeneous set, a vertex subset that induces a subgraph of minimum degree at least $t$ or the complement of such a graph.\n  For any $\\nu > 0$ and positive integer $k$, we show that any graph $G$ or its complement contains as an induced subgraph some graph $H$ on $\\ell \\ge k$ vertices with minimum degree at least $\\frac12(\\ell-1) + \\nu$ provided that $G$ has at least $k^{\\Omega(\\nu^2)}$ vertices. We also show this to be best possible in a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3464","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":""},"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"}