## Abstract

For natural numbers n, ∈ 2 ℕ with n ≥ r, the Kneser graph K (n, r) is the graph on the family of r-element subsets of {1; ⋯, 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 shall answer this question affirmatively as long as r/n is bounded away from 1/2, even when the probability of retaining an edge of the Kneser graph is quite small. This gives us a random analogue of the Erdos-Ko-Rado theorem, since an independent set in the Kneser graph is the same as a uniform intersecting family. To prove our main result, we give some new estimates for the number of disjoint pairs in a family in terms of its distance from an intersecting family; these might be of independent interest.

Original language | English (US) |
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Article number | e23 |

Pages (from-to) | e23, 18 |

Journal | Forum Math. Sigma |

Volume | 3 |

DOIs | |

State | Published - 2015 |

## ASJC Scopus subject areas

- Analysis
- Theoretical Computer Science
- Algebra and Number Theory
- Statistics and Probability
- Mathematical Physics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Mathematics