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The linear Tur\\'an number of $\\mathcal F$ is the maximum possible number of edges in a $3$-uniform linear hypergraph on $n$ vertices which contains no member of $\\mathcal{F}$ as a subhypergraph.\n  In this paper we show that the linear Tur\\'an number of the five cycle $C_5$ (in the Berge sense) is $\\frac{1}{3 \\sqrt3}n^{3/2}$ asymptotically. We also show that the linear Tur\\'an number of the four cycle $C_4$ and $\\{C_3, C_4\\}$ are equal asmptotically, which is a strengthening of a theorem of Lazebnik and Verstra\\\"ete.\n  We establis"},"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":"1705.03561","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-09T22:45:59Z","cross_cats_sorted":[],"title_canon_sha256":"27dfbdb962a59f473bd55b3525fb0ed4c188be2031faece4bd212bd93077f5c0","abstract_canon_sha256":"a1b7282c4727a712017bf0ad761e7234520540894d95ca4772323d73292ddab8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:05.725964Z","signature_b64":"JdFR8va0whJQA07XnR7cQt9JunmCa0CwY3zVW6whi9t45yUphzYu9YM+5NAqUY+2XytkebOhpwtp9+EffB9wAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1a2ef49478efa3505027280017eb4b3d5f2d46d15854c44478b092a40005eaa","last_reissued_at":"2026-05-18T00:05:05.725329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:05.725329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics for Tur\\'an numbers of cycles in 3-uniform linear hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Beka Ergemlidze, Ervin Gy\\H{o}ri","submitted_at":"2017-05-09T22:45:59Z","abstract_excerpt":"Let $\\mathcal{F}$ be a family of $3$-uniform linear hypergraphs. 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