{"paper":{"title":"On the Multi-coloured Ramsey Numbers of Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jozef Skokan, Mikl\\'os Simonovits, Tomasz {\\L}uczak","submitted_at":"2010-05-21T10:28:52Z","abstract_excerpt":"For a graph $L$ and an integer $k\\geq 2$, $R_k(L)$ denotes the smallest integer $N$ for which for any edge-colouring of the complete graph $K_N$ by $k$ colours there exists a colour $i$ for which the corresponding colour class contains $L$ as a subgraph.\n  Bondy and Erd\\H{o}s conjectured that for an odd cycle $C_n$ on $n$ vertices, $$R_k(C_n) = 2^{k-1}(n-1)+1 \\text{for $n>3$.}$$ They proved the case when $k=2$ and also provided an upper bound $R_k(C_n)\\leq (k+2)!n$. Recently, this conjecture has been verified for $k=3$ if $n$ is large. In this note, we prove that for every integer $k\\geq 4$, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3926","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"}