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In this note we focus on the case $n=3$. First, we compare the existing methods in this case and then improve the lower bound."},"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":"1905.02893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-07T13:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"f8d9d489a0a7608fa01059069c44c11f8a5d84470c3ef8fa0849042d34b7536c","abstract_canon_sha256":"b2fad42abbd79190e5e5beca7723f6e3b7046eaa96d855ede66ecfcd3f4c24ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:55.136896Z","signature_b64":"gO5bHaeoWF72wWLT9trbAGfkNT8qGw4NFF9Edz8aFUXUgCPEia4seT/VFpcIrajeJjbHQNmC0oUlrGceSS0lDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"102dd6377fe350c395e70662ef94f1d67ece04d0863a7971ce4577ec0585e688","last_reissued_at":"2026-05-17T23:40:55.136207Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:55.136207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Erd{\\H o}s--Hajnal problem in the case of 3-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danila Cherkashin","submitted_at":"2019-05-07T13:42:08Z","abstract_excerpt":"Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph which is not $r$-colorable. For the broad history of the problem see [RaiSh]. It is known that for a fixed $n$ the sequence \\[ \\frac{m(n,r)}{r^n} \\] has a limit.\n  The only trivial case is $n=2$ in which $m(2,r) = \\binom{r+1}{2}$. In this note we focus on the case $n=3$. 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