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We show that for such pseudo-random graphs the number of induced isomorphic copies of subgraphs of size $s$ are approximately same as that of an Erd\\H{o}s-R\\'{e}yni random graph with edge connectivity probability $p$ as long as $s \\le (((1-\\delta)\\wedge \\frac{1}{2})-o(1))\\log n/\\log ("},"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":"1610.03762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-12T15:56:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"672da3ebc6e01c7e0c18765c7c41386741f96ec1300dca492b87fe7853ded823","abstract_canon_sha256":"5811a879ab75258fa918898097b3b0dcccb6d2488db3b907bf2cb38491be2f2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:29.323088Z","signature_b64":"nfMELRim1CQXItxiqVdOTpucjpBIKAqPEMvYreEBAlUS19IqLe+A/JQwsAp7Ol2grS4Hx7Fha0nfC7g1tC+9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4e58d1765dea6c0e2149f20f3e312bbb1fd50fc161cc871bed5ff9198540315","last_reissued_at":"2026-05-18T01:02:29.322481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:29.322481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large subgraphs in pseudo-random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Andrew Nobel, Anirban Basak, Shankar Bhamidi, Suman Chakraborty","submitted_at":"2016-10-12T15:56:02Z","abstract_excerpt":"We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^\\delta,np+Cn^\\delta)$ and $(np^2- C n^\\delta, np^2 +C n^\\delta)$ respectively, for some absolute constant $C$, and $p, \\delta \\in (0,1)$. We show that for such pseudo-random graphs the number of induced isomorphic copies of subgraphs of size $s$ are approximately same as that of an Erd\\H{o}s-R\\'{e}yni random graph with edge connectivity probability $p$ as long as $s \\le (((1-\\delta)\\wedge \\frac{1}{2})-o(1))\\log n/\\log ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03762","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.03762","created_at":"2026-05-18T01:02:29.322570+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.03762v1","created_at":"2026-05-18T01:02:29.322570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03762","created_at":"2026-05-18T01:02:29.322570+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTSY2F3F32TM","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTSY2F3F32TMBYQU","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTSY2F3F","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO","json":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO.json","graph_json":"https://pith.science/api/pith-number/UTSY2F3F32TMBYQUT4QPHYYSXO/graph.json","events_json":"https://pith.science/api/pith-number/UTSY2F3F32TMBYQUT4QPHYYSXO/events.json","paper":"https://pith.science/paper/UTSY2F3F"},"agent_actions":{"view_html":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO","download_json":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO.json","view_paper":"https://pith.science/paper/UTSY2F3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.03762&json=true","fetch_graph":"https://pith.science/api/pith-number/UTSY2F3F32TMBYQUT4QPHYYSXO/graph.json","fetch_events":"https://pith.science/api/pith-number/UTSY2F3F32TMBYQUT4QPHYYSXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO/action/storage_attestation","attest_author":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO/action/author_attestation","sign_citation":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO/action/citation_signature","submit_replication":"https://pith.science/pith/UTSY2F3F32TMBYQUT4QPHYYSXO/action/replication_record"}},"created_at":"2026-05-18T01:02:29.322570+00:00","updated_at":"2026-05-18T01:02:29.322570+00:00"}