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When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well-known that the (sharp) threshold is at $p=1/n$. We consider a natural analogue of this question for higher-dimensional random complexes $X^k(n,p)$, first studied by Cohen, Costa, Farber and Kappeler for $k=2$.\n  Improving previous results, we show that $p=\\Theta(1/\\sqrt{n})$ is the (coarse) threshold for containing a subdivision of an"},"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":"1404.2106","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-08T12:36:25Z","cross_cats_sorted":["cs.DM","math.AT"],"title_canon_sha256":"cbf5fca7da9d8ae11e23e3f55868b3cbf86ef427d536608302a21396d0d63ff6","abstract_canon_sha256":"22bdbfcbaa27472c5d742a81199afa12768e9d1ed708e5bc4b92ae76bcc9a5e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:12.274826Z","signature_b64":"t+9U018/OmUCbAyA7y+LK92HYe7hhO0uuHqb2OpuGCVQcLojwhawwPGm66eMyNiL58zCAEbfChf5Rpv0WNa4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ce93be7c7c0f12f6268456dec4176fb974d291d65079a4e6ffb48835db72d29","last_reissued_at":"2026-05-18T02:17:12.274079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:12.274079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Topological Minors in Random Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.AT"],"primary_cat":"math.CO","authors_text":"Anna Gundert, Uli Wagner","submitted_at":"2014-04-08T12:36:25Z","abstract_excerpt":"For random graphs, the containment problem considers the probability that a binomial random graph $G(n,p)$ contains a given graph as a substructure. 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