{"paper":{"title":"On a Diagonal Conjecture for Classical Ramsey Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Meilian Liang, Stanis{\\l}aw Radziszowski, Xiaodong Xu","submitted_at":"2018-10-26T15:32:07Z","abstract_excerpt":"Let $R(k_1, \\cdots, k_r)$ denote the classical $r$-color Ramsey number for integers $k_i \\ge 2$. The Diagonal Conjecture (DC) for classical Ramsey numbers poses that if $k_1, \\cdots, k_r$ are integers no smaller than 3 and $k_{r-1} \\leq k_r$, then $R(k_1, \\cdots, k_{r-2}, k_{r-1}-1, k_r +1) \\leq R(k_1, \\cdots, k_r)$. We obtain some implications of this conjecture, present evidence for its validity, and discuss related problems.\n  Let $R_r(k)$ stand for the $r$-color Ramsey number $R(k, \\cdots, k)$. It is known that $\\lim_{r \\rightarrow \\infty} R_r(3)^{1/r}$ exists, either finite or infinite, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11386","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"}