### Abstract

The following dual version of Turán's problem is considered: for a given r-uniform hypergraph F, determine the minimum number of edges in an r-uniform hypergraph H on n vertices, such that F ⊄ H but a subhypergraph isomorphic to F occurs whenever a new edge (r-tuple) is added to H. For some types of F we find the exact value of the minimum or describe its asymptotic behavior as n tends to infinity; namely; for H_{r}(r + 1, r), H_{r}(2r -2, 2) and H_{r}(r + 1, 3), where H_{r}(p, q) denotes the family of all r-uniform hypergraphs with p vertices and q edges. Several problems remain open.

Original language | English |
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Pages (from-to) | 95-104 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 98 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 25 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Saturated r-uniform hypergraphs.** / Erdős, P.; Füredi, Z.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 98, no. 2, pp. 95-104. https://doi.org/10.1016/0012-365X(91)90035-Z

}

TY - JOUR

T1 - Saturated r-uniform hypergraphs

AU - Erdős, P.

AU - Füredi, Z.

AU - Tuza, Z.

PY - 1991/12/25

Y1 - 1991/12/25

N2 - The following dual version of Turán's problem is considered: for a given r-uniform hypergraph F, determine the minimum number of edges in an r-uniform hypergraph H on n vertices, such that F ⊄ H but a subhypergraph isomorphic to F occurs whenever a new edge (r-tuple) is added to H. For some types of F we find the exact value of the minimum or describe its asymptotic behavior as n tends to infinity; namely; for Hr(r + 1, r), Hr(2r -2, 2) and Hr(r + 1, 3), where Hr(p, q) denotes the family of all r-uniform hypergraphs with p vertices and q edges. Several problems remain open.

AB - The following dual version of Turán's problem is considered: for a given r-uniform hypergraph F, determine the minimum number of edges in an r-uniform hypergraph H on n vertices, such that F ⊄ H but a subhypergraph isomorphic to F occurs whenever a new edge (r-tuple) is added to H. For some types of F we find the exact value of the minimum or describe its asymptotic behavior as n tends to infinity; namely; for Hr(r + 1, r), Hr(2r -2, 2) and Hr(r + 1, 3), where Hr(p, q) denotes the family of all r-uniform hypergraphs with p vertices and q edges. Several problems remain open.

UR - http://www.scopus.com/inward/record.url?scp=0348096226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0348096226&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(91)90035-Z

DO - 10.1016/0012-365X(91)90035-Z

M3 - Article

AN - SCOPUS:0348096226

VL - 98

SP - 95

EP - 104

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

ER -