{"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"}