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In 1978, Erd\\H{o}s, Faudree, Rousseau and Schelp conjectured that $r(C_{\\ell},K_n) = (\\ell-1)(n-1)+1$ for $\\ell \\geq n\\geq 3$ provided $(\\ell,n) \\neq (3,3)$.\n  We prove that, for some absolute constant $C\\ge 1$, we have $r(C_{\\ell},K_n) = (\\ell-1)(n-1)+1$ provided $\\ell \\geq C\\frac {\\log n}{\\log \\log n}$. Up to the value of $C$ this is tight since we also show that, for any $\\varepsilon >0$ a","authors_text":"Eoin Long, Jozef Skokan, Peter Keevash","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T12:17:40Z","title":"Cycle-complete Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06376","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6c06e08e95e2c1ecc19053d51b3a22033ce93e72b2d2a4047aba65ca1b9ab763","target":"record","created_at":"2026-05-18T00:10:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ea6b0a132eb41cbf43da2fc3801e9c545f860195853e8c182dfe3f276003145d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T12:17:40Z","title_canon_sha256":"b626fad1e193e4b24173b9874093173db7fe3afa862500658835d66a08163080"},"schema_version":"1.0","source":{"id":"1807.06376","kind":"arxiv","version":1}},"canonical_sha256":"3e4f034a61869d2a81fd69885f7b1515b31c75851c322c2e8ad2c5fd43c63009","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e4f034a61869d2a81fd69885f7b1515b31c75851c322c2e8ad2c5fd43c63009","first_computed_at":"2026-05-18T00:10:33.207711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:33.207711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Kf26gcTUJFPm5FRkXAou4ASGyelohCFswsfT+QSdJZHKU30Oh8eOb7mjOsLwRpzCHwiDqv8vy0tTlgQ6JhpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:33.208273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c06e08e95e2c1ecc19053d51b3a22033ce93e72b2d2a4047aba65ca1b9ab763","sha256:c688a34144035cb1b8db99e144620fcfc6c67a7e611d1491a9b153244214d89d"],"state_sha256":"ce6e3401ba65e14662f3f49a85182d0e1aaf88d09df0097116f16b60e1dedcbe"}