{"paper":{"title":"The complexity of proving that a graph is Ramsey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Massimo Lauria, Neil Thapen, Pavel Pudl\\'ak, Vojt\\v{e}ch R\\\"odl","submitted_at":"2013-03-13T14:15:31Z","abstract_excerpt":"We say that a graph with $n$ vertices is $c$-Ramsey if it does not contain either a clique or an independent set of size $c \\log n$. We define a CNF formula which expresses this property for a graph $G$. We show a superpolynomial lower bound on the length of resolution proofs that $G$ is $c$-Ramsey, for every graph $G$. Our proof makes use of the fact that every Ramsey graph must contain a large subgraph with some of the statistical properties of the random graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3166","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":""},"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"}