## Abstract

A collection of sets is intersecting if every two members have nonempty intersection. We describe the structure of intersecting families of rsets of an n-set whose size is quite a bit smaller than the maximum (Formula presented) given by the Erdős-Ko-Rado Theorem. In particular, this extends the Hilton-Milner theorem on nontrivial intersecting families and answers a recent question of Han and Kohayakawa for large n. In the case r = 3 we describe the structure of all intersecting families with more than 10 edges. We also prove a stability result for the Erdős matching problem. Our short proofs are simple applications of the Delta-system method introduced and extensively used by Frankl since 1977.

Original language | English (US) |
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Pages (from-to) | 2311-2321 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 6 |

DOIs | |

State | Published - 2017 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics