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Our method also improves the best lower bounds for $r(C_{\\ell},t)$ obtained by Bohman and Keevash from the random $C_{\\ell}$-free process by polylogarithmic factors for all odd $\\ell \\geq 5$ and $\\ell \\in \\{6,10\\}$. For $\\ell = 4$ it matches their lower bound from the $C_4$-free process.\n  We also prove, via a different approach, that $r(C_5, t)> (1+o(1))t^{11/8}$ and $r(C_7, t)> (1+o(1))t^{11/9}$. These improve the exponent of $t$ in t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1909.01461","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-03T21:20:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e0969201d6f216f4634561943c03166d835793bbb0f540d2f1f2bbc573d30192","abstract_canon_sha256":"a530e6d260b2922e7bc21a3e114ab01fe92c1fd649527689fb1c105dee966655"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:07:52.951817Z","signature_b64":"bxs8ic/QYTUfYC0GXUe6ixI8xILFU9OExVhtSEH3sY2xCE2Urg1lyT/F8IkC9SrFGj+GSvaLtN4CxKpm1cKcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454e28b32acb081f08d31fdd86da65503b19c8854ae713fe81f39661e57117a8","last_reissued_at":"2026-07-05T00:07:52.951415Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:07:52.951415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on pseudorandom Ramsey graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Dhruv Mubayi, Jacques Verstraete","submitted_at":"2019-09-03T21:20:38Z","abstract_excerpt":"For fixed $s \\ge 3$, we prove that if optimal $K_s$-free pseudorandom graphs exist, then the Ramsey number\n  $r(s,t) = t^{s-1+o(1)}$ as $t \\rightarrow \\infty$. Our method also improves the best lower bounds for $r(C_{\\ell},t)$ obtained by Bohman and Keevash from the random $C_{\\ell}$-free process by polylogarithmic factors for all odd $\\ell \\geq 5$ and $\\ell \\in \\{6,10\\}$. For $\\ell = 4$ it matches their lower bound from the $C_4$-free process.\n  We also prove, via a different approach, that $r(C_5, t)> (1+o(1))t^{11/8}$ and $r(C_7, t)> (1+o(1))t^{11/9}$. 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