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- W4298515092 abstract "A family of sets is intersecting if no two of its members are disjoint, and has the ErdH{o}s-Ko-Rado property (or is EKR) if each of its largest intersecting subfamilies has nonempty intersection. Denote by $mathcal{H}_k(n,p)$ the random family in which each $k$-subset of ${1dots n}$ 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 $k< sqrt{cnlog n}$ we give a precise answer to this question, characterizing those sequences $p=p(n,k)$ for which $$ Pr(mathcal{H}_k(n,p) textrm{ is EKR}) rightarrow 1 textrm{ as } nrightarrow infty. $$" @default.
- W4298515092 created "2022-10-02" @default.
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- W4298515092 date "2014-12-16" @default.
- W4298515092 modified "2023-10-18" @default.
- W4298515092 title "On ErdH{o}s-Ko-Rado for random hypergraphs I" @default.
- W4298515092 doi "https://doi.org/10.48550/arxiv.1412.5085" @default.
- W4298515092 hasPublicationYear "2014" @default.
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