### Abstract

Given a family ℒ of graphs, set p =p(ℒ) = min_{ℒ∈ℒ} χ(L) - 1 and, for n≥ 1, denote by P(n,ℒ) the set of graphs with vertex set [n] containing no member of ℒ as a subgraph,and write ex(n,ℒ) for the maximal size of a member of P(n, ℒ). Extending a result of Erdos, Frankl and Rödl (Graphs Combin. 2 (1986) 113), we prove that A figure is presented. For some constant γ = γ(ℒ) > 0, and characterize γ in terms of some related extremal graph problems. In fact, if ex(n,ℒ) = O(n^{2-δ}), then any γ

Original language | English |
---|---|

Pages (from-to) | 1-24 |

Number of pages | 24 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 91 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2004 |

### Fingerprint

### Keywords

- Erdos-Kleitman-Rothschild theory
- Extremal graphs
- Speed function

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*91*(1), 1-24. https://doi.org/10.1016/j.jctb.2003.08.001

**The number of graphs without forbidden subgraphs.** / Balogh, József; Bollobás, Béla; Simonovits, M.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 91, no. 1, pp. 1-24. https://doi.org/10.1016/j.jctb.2003.08.001

}

TY - JOUR

T1 - The number of graphs without forbidden subgraphs

AU - Balogh, József

AU - Bollobás, Béla

AU - Simonovits, M.

PY - 2004/5

Y1 - 2004/5

N2 - Given a family ℒ of graphs, set p =p(ℒ) = minℒ∈ℒ χ(L) - 1 and, for n≥ 1, denote by P(n,ℒ) the set of graphs with vertex set [n] containing no member of ℒ as a subgraph,and write ex(n,ℒ) for the maximal size of a member of P(n, ℒ). Extending a result of Erdos, Frankl and Rödl (Graphs Combin. 2 (1986) 113), we prove that A figure is presented. For some constant γ = γ(ℒ) > 0, and characterize γ in terms of some related extremal graph problems. In fact, if ex(n,ℒ) = O(n2-δ), then any γ

AB - Given a family ℒ of graphs, set p =p(ℒ) = minℒ∈ℒ χ(L) - 1 and, for n≥ 1, denote by P(n,ℒ) the set of graphs with vertex set [n] containing no member of ℒ as a subgraph,and write ex(n,ℒ) for the maximal size of a member of P(n, ℒ). Extending a result of Erdos, Frankl and Rödl (Graphs Combin. 2 (1986) 113), we prove that A figure is presented. For some constant γ = γ(ℒ) > 0, and characterize γ in terms of some related extremal graph problems. In fact, if ex(n,ℒ) = O(n2-δ), then any γ

KW - Erdos-Kleitman-Rothschild theory

KW - Extremal graphs

KW - Speed function

UR - http://www.scopus.com/inward/record.url?scp=2342449349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2342449349&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2003.08.001

DO - 10.1016/j.jctb.2003.08.001

M3 - Article

AN - SCOPUS:2342449349

VL - 91

SP - 1

EP - 24

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 1

ER -