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A main ingredient in our proof is an induced variant of Mader's theorem: for every fixed \\(s,\\eta,D\\), every graph \\(J\\) with \\(\\Delta(J)\\le D\\), \\(d(J)>s-2+\\eta\\) and sufficiently large girth contains an induced subdivision of \\(K_s\\)."},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.17218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T01:32:55Z","cross_cats_sorted":[],"title_canon_sha256":"4ddc4dd9fcab9d21e2bca0fca9d5750345e079d6256c0dc8a8ddec02fdc42355","abstract_canon_sha256":"0bd977e92df77531511b8137219735cbbfede865001be27a1b4169a4b4cd61ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:45.797985Z","signature_b64":"bgpzPrf4EBZIyU7nT40V8AVHc60kodCFYb3mYimyPlT0ZCuF+OgSS7FzX1/+QC/7VKt0Typ6tSFw75VKLaVsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd18f52f08be57350483bc328e34705e2fa79cdc1eea343af950f485479e4a5f","last_reissued_at":"2026-05-20T00:03:45.796918Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:45.796918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced subdivisions in graphs of large girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peiru Kuang, Yan Wang","submitted_at":"2026-05-17T01:32:55Z","abstract_excerpt":"In this paper, we prove that there exists an absolute constant $g_0$ such that, for every integer $k\\ge 3$, every graph $G$ with $\\delta(G)\\ge k$ and $g(G)\\ge g_0$ contains an induced subdivision of $K_{k+1}$. 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