{"paper":{"title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arran Hamm, Jeff Kahn","submitted_at":"2014-06-23T02:19:31Z","abstract_excerpt":"Denote by $\\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset of $\\{1... n\\}$ is present with probability $p$, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed $\\varepsilon >0$ such that if $n=2k+1$ and $p> 1-\\varepsilon$, then w.h.p. (that is, with probability tending to 1 as $k\\rightarrow \\infty$), $\\mathcal{H}_k (n,p)$ has the \"Erd\\H{o}s-Ko-Rado property.\" We also mention a similar random version of Sperner's Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5793","kind":"arxiv","version":3},"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"}