{"paper":{"title":"An explicit Ramsey graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'abor Heged\\\"us","submitted_at":"2014-12-08T10:28:53Z","abstract_excerpt":"Explicit construction of Ramsey graphs has remained a challenging open problem for a long time. Frankl--Wilson \\cite{FW}, Alon \\cite{A} and Grolmusz \\cite{G2} gave the best explicit constructions of graphs on $m$ vertices with no clique or independent set of size $m^{(1+o(1))\\frac{1}{4}\\frac{\\log m}{\\log \\log m}}$.\n  We describe here an explicit construction which produces for every integer $m>1$ a graph on at least $m^{(1+o(1))\\frac{1}{3}\\frac{\\log m}{\\log \\log m}}$ vertices containing neither a clique of size $m$ nor an independent set of size $m$. In the proof we use the polynomial subspace"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2504","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"}