### Abstract

Suppose S is a Steiner triple-system on the n-element set X, i.e., for every pair of distinct vertices of X there is exactly one triple in S containing them. Necessarily, |S| = n(n - 1)/6 holds. It is easy to see that, for S, T, S′, T′ ∈ S, S ∪ T = S′ ∪ T′ implies {S, T} = {S′, T′}. We show that, conversely, this condition, for any family S′ of 3-subsets of X, implies |S′| ≤ n(n - 1)/6. A similar type of result is obtained for a weaker union condition. The corresponding problems for graphs are still open.

Original language | English |
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Pages (from-to) | 205-212 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 48 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1984 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*48*(2-3), 205-212. https://doi.org/10.1016/0012-365X(84)90183-3

**A new extremal property of Steiner triple-systems.** / Frankl, P.; Füredi, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 48, no. 2-3, pp. 205-212. https://doi.org/10.1016/0012-365X(84)90183-3

}

TY - JOUR

T1 - A new extremal property of Steiner triple-systems

AU - Frankl, P.

AU - Füredi, Z.

PY - 1984

Y1 - 1984

N2 - Suppose S is a Steiner triple-system on the n-element set X, i.e., for every pair of distinct vertices of X there is exactly one triple in S containing them. Necessarily, |S| = n(n - 1)/6 holds. It is easy to see that, for S, T, S′, T′ ∈ S, S ∪ T = S′ ∪ T′ implies {S, T} = {S′, T′}. We show that, conversely, this condition, for any family S′ of 3-subsets of X, implies |S′| ≤ n(n - 1)/6. A similar type of result is obtained for a weaker union condition. The corresponding problems for graphs are still open.

AB - Suppose S is a Steiner triple-system on the n-element set X, i.e., for every pair of distinct vertices of X there is exactly one triple in S containing them. Necessarily, |S| = n(n - 1)/6 holds. It is easy to see that, for S, T, S′, T′ ∈ S, S ∪ T = S′ ∪ T′ implies {S, T} = {S′, T′}. We show that, conversely, this condition, for any family S′ of 3-subsets of X, implies |S′| ≤ n(n - 1)/6. A similar type of result is obtained for a weaker union condition. The corresponding problems for graphs are still open.

UR - http://www.scopus.com/inward/record.url?scp=3142529726&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142529726&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(84)90183-3

DO - 10.1016/0012-365X(84)90183-3

M3 - Article

VL - 48

SP - 205

EP - 212

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2-3

ER -