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We show that if $\\alpha<1$ then whp the maximum component size of $G_p$ is $O(\\log n)$ and if $\\alpha>1$ then $G_p$ contains a unique giant component of size $\\Omega(n)$, with all other components of size $O(\\log n)$."},"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":"1605.06643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-21T13:40:46Z","cross_cats_sorted":[],"title_canon_sha256":"2feabe3fe2588aae0c7869127d2da773f579a8f9763416b5582b58e197dde51f","abstract_canon_sha256":"f02391d85317044b01303586a86aee9a1c09a4906ce2c959e1445c4c89966e19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:46.735395Z","signature_b64":"cpY61uSsqkWJHGnjfeqqzznNwfg86xwR+ivs918nFaLjnBWKw6w0MWHeFle5o97YexfM01/ZRUxqRn4tUAO5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e74c6261673b1d9de5827db921267bb96d24ea40bf280dacf32b824df639f2c","last_reissued_at":"2026-05-18T01:13:46.734647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:46.734647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The emergence of a giant component in random subgraphs of pseudo-random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Michael Krivelevich, Ryan R. 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