{"paper":{"title":"New bounds for the distance Ramsey number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrei Raigorodskii, Andrey Kupavskii, Maria Titova","submitted_at":"2013-07-02T20:48:06Z","abstract_excerpt":"In this paper we study the distance Ramsey number $R_{{\\it D}}(s,t,d)$. The \\textit{distance Ramsey number} $R_{{\\it D}}(s,t,d) $ is the minimum number $n$ such that for any graph $ G $ on $ n $ vertices, either $G$ contains an induced $ s $-vertex subgraph isomorphic to a distance graph in $ \\Real^d $ or $ \\bar {G} $ contains an induced $ t $-vertex subgraph isomorphic to the distance graph in $ \\Real^d $. We obtain the upper and lower bounds on $R_{{\\it D}}(s,s,d),$ which are similar to the bounds for the classical Ramsey number $R(\\lceil \\frac{s}{[d/2]} \\rceil, \\lceil \\frac{s}{[d/2]} \\rceil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0843","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"}