{"paper":{"title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arran Hamm, Jeff Kahn","submitted_at":"2014-12-16T17:10:17Z","abstract_excerpt":"A family of sets is intersecting if no two of its members are disjoint, and has the Erd\\H{o}s-Ko-Rado property (or is EKR) if each of its largest intersecting subfamilies has nonempty intersection.\n  Denote by $\\mathcal{H}_k(n,p)$ the random family in which each $k$-subset of $\\{1\\dots n\\}$ is present with probability $p$, independent of other choices. A question first studied by Balogh, Bohman and Mubayi asks: \\[ \\mbox{for what $p=p(n,k)$ is $\\mathcal{H}_k(n,p)$ likely to be EKR?} \\] Here, for fixed $c<1/4$, and $k< \\sqrt{cn\\log n}$ we give a precise answer to this question, characterizing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5085","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"}