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Let $s,t,k\\geq 2$ be integers. Let $K_{s,t}^k$ denote the graph obtained from the complete bipartite graph $K_{s,t}$ by replacing each edge $uv$ in it with a path of length $k$ between $u$ and $v$ such that the $st$ replacing paths are internally disjoint. It follows from a general theore"},"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":"1905.08994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-22T07:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"f9f5e152abb357617471aae2bb768310b7fb0714e775c95f07a597c3feed0e30","abstract_canon_sha256":"2e766a620e590b980049da299c5d76d892071b227eb0203d5bccc6f9e200a922"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:37.472537Z","signature_b64":"/kO2c/C7oXZO8uT1HGIm2Q/jC7iSeFwPU5v2k4QLiEAuFALjVDumiYP23cODCKk94j+suy1G7UhN5BzJLbWUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9036113a8ec9dc8bbd727c77460f785f801f7d7b2fa78864cc968a462aed1315","last_reissued_at":"2026-05-17T23:44:37.472039Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:37.472039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Turan numbers of bipartite subdivisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tao Jiang, Yu Qiu","submitted_at":"2019-05-22T07:32:40Z","abstract_excerpt":"Given a graph $H$, the Tur\\'an number $ex(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a recent conjecture of Conlon, Janzer, and Lee on the Tur\\'an numbers of bipartite graphs, which in turn yields further progress on a conjecture of Erd\\H{o}s and Simonovits. Let $s,t,k\\geq 2$ be integers. Let $K_{s,t}^k$ denote the graph obtained from the complete bipartite graph $K_{s,t}$ by replacing each edge $uv$ in it with a path of length $k$ between $u$ and $v$ such that the $st$ replacing paths are internally disjoint. 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