{"paper":{"title":"Full subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jacques Verstra\\\"ete, Klas Markstr\\\"om, Victor Falgas-Ravry","submitted_at":"2015-05-12T15:58:41Z","abstract_excerpt":"Let $G=(V,E)$ be a graph of density $p$ on $n$ vertices. 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03072","kind":"arxiv","version":2},"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"}