{"paper":{"title":"Generalised Ramsey numbers for two sets of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mikael Hansson","submitted_at":"2016-05-13T19:47:22Z","abstract_excerpt":"We determine several generalised Ramsey numbers for two sets $\\Gamma_1$ and $\\Gamma_2$ of cycles, in particular, all generalised Ramsey numbers $R(\\Gamma_1,\\Gamma_2)$ such that $\\Gamma_1$ or $\\Gamma_2$ contains a cycle of length at most $6$, or the shortest cycle in each set is even. This generalises previous results of Erd\\H{o}s, Faudree, Rosta, Rousseau, and Schelp from the 1970s. Notably, including both $C_3$ and $C_4$ in one of the sets, makes very little difference from including only $C_4$. Furthermore, we give a conjecture for the general case. We also describe many $(\\Gamma_1,\\Gamma_2)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04301","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"}