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It is shown that asymptotically almost surely $AC(G) = O(\\log n / p)$ for $G \\in G(n,p)$, provided that $pn > (1+\\epsilon) \\log n$ for some $\\epsilon > 0$ (slightly above the threshold for connectivity). Moreover, we show a matching lower bound for dense random graphs, which also implies that asymptotically almost surely $K_n$ cannot be covered with $o(\\log n / p)$ copies of a random graph $G \\in G(n,p)$, provided that $pn > n^{1/2+\\epsilon}$ and $p < 1"},"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":"1305.1675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-07T23:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"5f3856192d584697aed5fe146d42259ef5eac40c875ebd021f119b4f95ec6b4d","abstract_canon_sha256":"5d4101f212f7cd2bf5edf75fb1d3a0407ac60c77ff32bd7fe8b708f6eea69b21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:00.944026Z","signature_b64":"H+YoJR+Y7JI39F8UcxhSSBp8eBRKwYCRDtCdGsaH1OFQfdB6ZOHXziDY3dq7F2XhsSHgXMWNVpJwueg+0GEiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8c2451410a88a2e67d77dc28f5c72b9c4486e55131171cf29efe4e28fdf610","last_reissued_at":"2026-05-18T02:50:00.943519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:00.943519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the acquaintance time of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. 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