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Following Erd\\H{o}s, \\L uczak and Spencer, an $m$-vertex subgraph $H$ of $G$ is called {\\em full} if $H$ has minimum degree at least $p(m - 1)$. Let $f(G)$ denote the order of a largest full subgraph of $G$. If $p\\binom{n}{2}$ is a non-negative integer, define \\[ f(n,p) = \\min\\{f(G) : \\vert V(G)\\vert = n, \\ \\vert E(G)\\vert = p\\binom{n}{2} \\}.\\] Erd\\H{o}s, \\L uczak and Spencer proved that for $n \\geq 2$, \\[ (2n)^{\\frac{1}{2}} - 2 \\leq f(n, {\\frac{1}{2}}) \\leq 4n^{\\frac{2}{3}}(\\log n)^{\\frac{1}{3}}.\\] In this paper, we prove the following ","authors_text":"Jacques Verstra\\\"ete, Klas Markstr\\\"om, Victor Falgas-Ravry","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-12T15:58:41Z","title":"Full subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03072","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3b0555c0ae3076a8d3c706fe015c7a13464f6d4c9a1f65e5e51e2322d74e6ffb","target":"record","created_at":"2026-05-18T01:01:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e49afb80fd1d369aac90b348f95809de1a014c8289d6af4868bc76ce6b271a7a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-12T15:58:41Z","title_canon_sha256":"948a5d4fc25202f42769a0a8cd960ac38a1f0f22248c32c71ecab163e0a100ec"},"schema_version":"1.0","source":{"id":"1505.03072","kind":"arxiv","version":2}},"canonical_sha256":"50c2d823ff1ae9927293c2f6fb8b08222c779a0086c98edf840199432912c4ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50c2d823ff1ae9927293c2f6fb8b08222c779a0086c98edf840199432912c4ab","first_computed_at":"2026-05-18T01:01:42.386876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:42.386876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V3N/5917sc5c4jbmzWTKt7hxoK1s1hPvrUnC6fCi86q+SUy6aON3YUxhdP9Cp5w7WMOpZLkVkdcx6QFjVwhjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:42.387436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03072","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b0555c0ae3076a8d3c706fe015c7a13464f6d4c9a1f65e5e51e2322d74e6ffb","sha256:96dad3ca779f04de068ccd1e5540f2d9ab51701612f9903b250e253eb55792f4"],"state_sha256":"18efb30a9da1049ce5f4efdd0c40b948d620937dd091c772d52b9646159ebdbd"}