### 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 |
---|---|

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 - 1986 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*40*(3), 270-284. https://doi.org/10.1016/0095-8956(86)90084-5

**Extremal problems concerning Kneser graphs.** / Frankl, P.; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 40, no. 3, pp. 270-284. https://doi.org/10.1016/0095-8956(86)90084-5

}

TY - JOUR

T1 - Extremal problems concerning Kneser graphs

AU - Frankl, P.

AU - Füredi, Z.

PY - 1986

Y1 - 1986

N2 - Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-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))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

AB - Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-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))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

UR - http://www.scopus.com/inward/record.url?scp=38249039814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249039814&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(86)90084-5

DO - 10.1016/0095-8956(86)90084-5

M3 - Article

AN - SCOPUS:38249039814

VL - 40

SP - 270

EP - 284

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -