{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:50:47Z","timestamp":1773103847081,"version":"3.50.1"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T00:00:00Z","timestamp":1539820800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Denote by<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548318000433_inline1\"\/><jats:tex-math>${\\mathcal H}_k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>n<\/jats:italic>,<jats:italic>p<\/jats:italic>) the random<jats:italic>k<\/jats:italic>-graph in which each<jats:italic>k<\/jats:italic>-subset of {1,.\u00a0.\u00a0.,<jats:italic>n<\/jats:italic>} is present with probability<jats:italic>p<\/jats:italic>, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed \u03b5 &gt; 0 such that if<jats:italic>n<\/jats:italic>= 2<jats:italic>k<\/jats:italic>+ 1 and<jats:italic>p<\/jats:italic>&gt; 1 - \u03b5, then w.h.p. (that is, with probability tending to 1 as<jats:italic>k<\/jats:italic>\u2192 \u221e),<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548318000433_inline1\"\/><jats:tex-math>${\\mathcal H}_k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>n<\/jats:italic>,<jats:italic>p<\/jats:italic>) has the \u2018Erd\u0151s\u2013Ko\u2013Rado property\u2019. We also mention a similar random version of Sperner's theorem.<\/jats:p>","DOI":"10.1017\/s0963548318000433","type":"journal-article","created":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T05:29:11Z","timestamp":1539840551000},"page":"61-80","source":"Crossref","is-referenced-by-count":6,"title":["On Erd\u0151s\u2013Ko\u2013Rado for Random Hypergraphs II"],"prefix":"10.1017","volume":"28","author":[{"given":"A.","family":"HAMM","sequence":"first","affiliation":[]},{"given":"J.","family":"KAHN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,10,18]]},"reference":[{"key":"S0963548318000433_ref30","doi-asserted-by":"publisher","DOI":"10.4064\/aa-27-1-199-245"},{"key":"S0963548318000433_ref23","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"S0963548318000433_ref28","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2016.184.2.1"},{"key":"S0963548318000433_ref20","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1525\/9780520319875-014","volume-title":"Mathematical Optimization Techniques","author":"Kruskal","year":"1963"},{"key":"S0963548318000433_ref10","unstructured":"DeMarco R. and Kahn, J. 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