On the stability of the Erdős-Ko-Rado theorem

Béla Bollobás, Bhargav Narayanan, Andrei Raigorodskii

Published 2014-08-06, updated 2016-09-06Version 2

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 a uniform intersecting family, this gives us a random analogue of the Erd\H{o}s-Ko-Rado theorem.