Abstract
Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the Kneser graph itself? We prove a sharp threshold result for this question in certain regimes. Since an independent set in the Kneser graph is the same as an intersecting (uniform) family, this gives us a random analogue of the Erdős–Ko–Rado theorem.
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