### Abstract

Let H^{ r} be an r-uniform hypergraph. Let g=g(n;H^{ r} ) be the minimal integer so that any r-uniform hypergraph on n vertices and more than g edges contains a subgraph isomorphic to H^{ r} . Let e =f(n;H^{ r}, εn) denote the minimal integer such that every r-uniform hypergraph on n vertices with more than e edges and with no independent set of εn vertices contains a subgraph isomorphic to H^{ r} . We show that if r>2 and H^{ r} is e.g. a complete graph then {Mathematical expression} while for some H^{ r} with {Mathematical expression} {Mathematical expression}. This is in strong contrast with the situation in case r=2. Some other theorems and many unsolved problems are stated.

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

Pages (from-to) | 289-295 |

Number of pages | 7 |

Journal | Combinatorica |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1982 |

### Fingerprint

### Keywords

- AMS subject classification (1980): 05C65, 05C35, 05C55

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

*2*(3), 289-295. https://doi.org/10.1007/BF02579235

**On Ramsey-Turán type theorems for hypergraphs.** / Erdős, P.; Sós, Vera T.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 2, no. 3, pp. 289-295. https://doi.org/10.1007/BF02579235

}

TY - JOUR

T1 - On Ramsey-Turán type theorems for hypergraphs

AU - Erdős, P.

AU - Sós, Vera T.

PY - 1982/9

Y1 - 1982/9

N2 - Let H r be an r-uniform hypergraph. Let g=g(n;H r ) be the minimal integer so that any r-uniform hypergraph on n vertices and more than g edges contains a subgraph isomorphic to H r . Let e =f(n;H r, εn) denote the minimal integer such that every r-uniform hypergraph on n vertices with more than e edges and with no independent set of εn vertices contains a subgraph isomorphic to H r . We show that if r>2 and H r is e.g. a complete graph then {Mathematical expression} while for some H r with {Mathematical expression} {Mathematical expression}. This is in strong contrast with the situation in case r=2. Some other theorems and many unsolved problems are stated.

AB - Let H r be an r-uniform hypergraph. Let g=g(n;H r ) be the minimal integer so that any r-uniform hypergraph on n vertices and more than g edges contains a subgraph isomorphic to H r . Let e =f(n;H r, εn) denote the minimal integer such that every r-uniform hypergraph on n vertices with more than e edges and with no independent set of εn vertices contains a subgraph isomorphic to H r . We show that if r>2 and H r is e.g. a complete graph then {Mathematical expression} while for some H r with {Mathematical expression} {Mathematical expression}. This is in strong contrast with the situation in case r=2. Some other theorems and many unsolved problems are stated.

KW - AMS subject classification (1980): 05C65, 05C35, 05C55

UR - http://www.scopus.com/inward/record.url?scp=51249186532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249186532&partnerID=8YFLogxK

U2 - 10.1007/BF02579235

DO - 10.1007/BF02579235

M3 - Article

AN - SCOPUS:51249186532

VL - 2

SP - 289

EP - 295

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 3

ER -