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Erd\\H{o}s and Simonovits \\cite{ESi1} conjectured that for every family $\\mathcal{F}$ of bipartite graphs, there exists $k$ such that $\\ex{n}{\\mathcal{F} \\cup \\mathcal{C}_k} \\sim \\ex{n}{\\mathcal{F} \\cup \\mathcal{C}}$ as $n \\rightarrow \\infty$. This conjecture was proved by Erd\\H{o}s and Simonovits when $\\mathcal{F} = \\{C_4\\}$, and for certain families of even cycles in \\cite{KSV}. In this paper, we give a general a"},"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":"1210.3805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-14T15:38:38Z","cross_cats_sorted":[],"title_canon_sha256":"53feb17fb9e1fc7c23069a02f46f6ec25bc24a2c778e8cf4b8205e5b387801f6","abstract_canon_sha256":"8ddb588449164bfeb4698d2c531b1d89aa27a65faeb57116d555c3cdb29741c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:17.058947Z","signature_b64":"5PVmv/hsKVU3Ks5z4gFxbHg34d60LYmejUcZP53AjLgkWBC7ZNvtc575hvH422U+mZHrJFa0EMyL7ZqKdoJTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cc6619ca12d3792ccc3a5b2834cd1360d630410f56968a979ea04c590c89f97","last_reissued_at":"2026-05-18T03:43:17.058210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:17.058210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Turan numbers for bipartite graphs plus an odd cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Jacques Verstraete, Peter Allen, Peter Keevash","submitted_at":"2012-10-14T15:38:38Z","abstract_excerpt":"For an odd integer $k$, let $\\mathcal{C}_k = \\{C_3,C_5,...,C_k\\}$ denote the family of all odd cycles of length at most $k$ and let $\\mathcal{C}$ denote the family of all odd cycles. Erd\\H{o}s and Simonovits \\cite{ESi1} conjectured that for every family $\\mathcal{F}$ of bipartite graphs, there exists $k$ such that $\\ex{n}{\\mathcal{F} \\cup \\mathcal{C}_k} \\sim \\ex{n}{\\mathcal{F} \\cup \\mathcal{C}}$ as $n \\rightarrow \\infty$. This conjecture was proved by Erd\\H{o}s and Simonovits when $\\mathcal{F} = \\{C_4\\}$, and for certain families of even cycles in \\cite{KSV}. 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