• Corpus ID: 119671539

Transference for the Erd\H{o}s-Ko-Rado theorem

  title={Transference for the Erd\H\{o\}s-Ko-Rado theorem},
  author={J{\'o}zsef Balogh and B'ela Bollob'as and Bhargav P. Narayanan},
  journal={arXiv: Combinatorics},
For natural numbers $n,r \in \mathbb{N}$ with $n\ge r$, the Kneser graph $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\dots,n\}$ in which two sets are adjacent if and only if they are disjoint. Delete the edges of $K(n,r)$ with some probability, independently of each other: is the independence number of this random graph equal to the independence number of the Kneser graph itself? We answer this question affirmatively as long as $r/n$ is bounded away from $1/2$, even when… 
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