{"paper":{"title":"A generalized Tur\\'an problem in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Clara Shikhelman, Wojciech Samotij","submitted_at":"2018-06-18T12:00:27Z","abstract_excerpt":"We study the following generalization of the Tur\\'an problem in sparse random graphs. Given graphs $T$ and $H$, let $\\mathrm{ex}\\big(G(n,p), T, H\\big)$ be the random variable that counts the largest number of copies of $T$ in a subgraph of $G(n,p)$ that does not contain $H$. We study the threshold phenomena arising in the evolution of the typical value of this random variable, for every $H$ and an arbitrary $2$-balanced $T$.\n  Our results in the case when $m_2(H) > m_2(T)$ are a natural generalization of the Erd\\H{o}s--Stone theorem for $G(n,p)$, which was proved several years ago by Conlon an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06609","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"}