### Abstract

A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order 2. Proving a conjecture of T. Sós, the largest triple system on n vertices containing no Fano configuration is determined (for n > n_{1}). It is 2-chromatic with (n_{3}) - ([n/2]_{3}) - ([n/2]_{3}) triples. This is one of the very few nontrivial exact results for hypergraph extremal problems.

Original language | English |
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Pages (from-to) | 467-484 |

Number of pages | 18 |

Journal | Combinatorics Probability and Computing |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Statistics and Probability

### Cite this

**Triple systems not containing a fano configuration.** / Füredi, Z.; Simonovits, M.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 14, no. 4, pp. 467-484. https://doi.org/10.1017/S0963548305006784

}

TY - JOUR

T1 - Triple systems not containing a fano configuration

AU - Füredi, Z.

AU - Simonovits, M.

PY - 2005/7

Y1 - 2005/7

N2 - A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order 2. Proving a conjecture of T. Sós, the largest triple system on n vertices containing no Fano configuration is determined (for n > n1). It is 2-chromatic with (n3) - ([n/2]3) - ([n/2]3) triples. This is one of the very few nontrivial exact results for hypergraph extremal problems.

AB - A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order 2. Proving a conjecture of T. Sós, the largest triple system on n vertices containing no Fano configuration is determined (for n > n1). It is 2-chromatic with (n3) - ([n/2]3) - ([n/2]3) triples. This is one of the very few nontrivial exact results for hypergraph extremal problems.

UR - http://www.scopus.com/inward/record.url?scp=23844540761&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23844540761&partnerID=8YFLogxK

U2 - 10.1017/S0963548305006784

DO - 10.1017/S0963548305006784

M3 - Article

AN - SCOPUS:23844540761

VL - 14

SP - 467

EP - 484

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 4

ER -