### Abstract

Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (_{k-1}^{n-1}) + (_{k-1}^{n-1}) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(_{k}^{n}) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

Original language | English |
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Pages (from-to) | 270-284 |

Number of pages | 15 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 40 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 1986 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Frankl, P., & Füredi, Z. (1986). Extremal problems concerning Kneser graphs.

*Journal of Combinatorial Theory, Series B*,*40*(3), 270-284. https://doi.org/10.1016/0095-8956(86)90084-5