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The lower bound is due to Radhakrishnan and Srinivasan (see \\cite{RS}). A natural generalization for $ m(n) $ is the quantity $ m(n,r) $, which is the minimum number of edges in an $n$-uniform hypergraph with chromatic number at least $r+1$. In this work, we present a new randomized algorithm yielding a bound $ m(n,r) \\ge c"},"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":"1308.6696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-30T09:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"f53b5c01b45c7b784032e5b4ed4e5a51117c6334f87e212bf2602903d2cee768","abstract_canon_sha256":"e3572ddcf93c86564ec475bbeed52ba20492fb9a924afc9295487b8f153d262c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:38.375671Z","signature_b64":"rTbSShefiSdLTq1JKuNFk4Tdlby3QebmjP9FcOZon4VYC9OVRTw8cwUg0clnLBZ/VnpuV8g3wl8O7lDbYSVnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"503305cd65957dbca70be6dddc166f7ca959b019dcf1cff88864831dc7d130c4","last_reissued_at":"2026-05-18T03:14:38.375218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:38.375218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new randomized algorithm for the Erdos--Hajnal problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danila Cherkashin","submitted_at":"2013-08-30T09:53:22Z","abstract_excerpt":"In 1961 Erd\\H{o}s and Hajnal introduced the quantity $m(n)$ as the minimum number of edges in an $n$-uniform hypergraph with chromatic number at least 3. 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