### Abstract

Let H be a fixed graph of chromatic number r. It is shown that the number of graphs on n vertices and not containing H as a subgraph is {Mathematical expression}. Let h_{r}(n) denote the maximum number of edges in an r-uniform hypergraph on n vertices and in which the union of any three edges has size greater than 3 r - 3. It is shown that h_{r}(n) =o(n^{2}) although for every fixed c <2 one has lim_{n→∞}h_{r}(n)/n^{c} = ∞.

Original language | English |
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Pages (from-to) | 113-121 |

Number of pages | 9 |

Journal | Graphs and Combinatorics |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1986 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Graphs and Combinatorics*,

*2*(1), 113-121. https://doi.org/10.1007/BF01788085

**The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent.** / Erdős, P.; Frankl, P.; Rödl, V.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 2, no. 1, pp. 113-121. https://doi.org/10.1007/BF01788085

}

TY - JOUR

T1 - The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent

AU - Erdős, P.

AU - Frankl, P.

AU - Rödl, V.

PY - 1986/12

Y1 - 1986/12

N2 - Let H be a fixed graph of chromatic number r. It is shown that the number of graphs on n vertices and not containing H as a subgraph is {Mathematical expression}. Let hr(n) denote the maximum number of edges in an r-uniform hypergraph on n vertices and in which the union of any three edges has size greater than 3 r - 3. It is shown that hr(n) =o(n2) although for every fixed c <2 one has limn→∞hr(n)/nc = ∞.

AB - Let H be a fixed graph of chromatic number r. It is shown that the number of graphs on n vertices and not containing H as a subgraph is {Mathematical expression}. Let hr(n) denote the maximum number of edges in an r-uniform hypergraph on n vertices and in which the union of any three edges has size greater than 3 r - 3. It is shown that hr(n) =o(n2) although for every fixed c <2 one has limn→∞hr(n)/nc = ∞.

UR - http://www.scopus.com/inward/record.url?scp=0011319584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011319584&partnerID=8YFLogxK

U2 - 10.1007/BF01788085

DO - 10.1007/BF01788085

M3 - Article

VL - 2

SP - 113

EP - 121

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 1

ER -