### Abstract

The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assume k≧2, ε>0, G_{ n} is a sequence of graphs of n-vertices and at least 1/2((3 k-5) / (3 k-2)+ε)n^{ 2} edges, and the size of the largest independent set in G_{ n} is o(n). Let H be any graph of arboricity at most k. Then there exists an n_{ 0} such that all G_{ n} with n>n_{ 0} contain a copy of H. This result is best possible in case H=K_{ 2 k} .

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

Pages (from-to) | 69-81 |

Number of pages | 13 |

Journal | Combinatorica |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1983 |

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### Keywords

- AMS subject classification (1980): 05C55, 05C35

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

*3*(1), 69-81. https://doi.org/10.1007/BF02579342

**More results on Ramsey-Turán type problems.** / Erdős, P.; Hajnal, A.; Sós, Vera T.; Szemerédi, E.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 3, no. 1, pp. 69-81. https://doi.org/10.1007/BF02579342

}

TY - JOUR

T1 - More results on Ramsey-Turán type problems

AU - Erdős, P.

AU - Hajnal, A.

AU - Sós, Vera T.

AU - Szemerédi, E.

PY - 1983/3

Y1 - 1983/3

N2 - The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assume k≧2, ε>0, G n is a sequence of graphs of n-vertices and at least 1/2((3 k-5) / (3 k-2)+ε)n 2 edges, and the size of the largest independent set in G n is o(n). Let H be any graph of arboricity at most k. Then there exists an n 0 such that all G n with n>n 0 contain a copy of H. This result is best possible in case H=K 2 k .

AB - The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assume k≧2, ε>0, G n is a sequence of graphs of n-vertices and at least 1/2((3 k-5) / (3 k-2)+ε)n 2 edges, and the size of the largest independent set in G n is o(n). Let H be any graph of arboricity at most k. Then there exists an n 0 such that all G n with n>n 0 contain a copy of H. This result is best possible in case H=K 2 k .

KW - AMS subject classification (1980): 05C55, 05C35

UR - http://www.scopus.com/inward/record.url?scp=51249181997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249181997&partnerID=8YFLogxK

U2 - 10.1007/BF02579342

DO - 10.1007/BF02579342

M3 - Article

VL - 3

SP - 69

EP - 81

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -