### Abstract

Extremal graph theory, Ramsey theory and the theory of Random graphs are strongly connected to each other. Starting from these fields, we formulate some problems and results which are related to different levels of randomness. The first one is completely non-random, being the ordinary Ramsey-Turán problem and in the subsequent three problems we formulate some randomized variations of the problem. Speaking of graph properties, we shall consider them as sets of graphs and occasionally write G ∈ P instead of writing that G has property P. A graph property P is called monotone if adding an edge to a H_{n} ∈ P, we get an H^{*}_{n} ∈ P. We shall use three models of random graphs: the binomial, the hypergeometric and the stopping-rule model. This abstract contains the most important definitions.

Original language | English |
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Pages (from-to) | 189-192 |

Number of pages | 4 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 15 |

DOIs | |

Publication status | Published - May 2003 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*15*, 189-192. https://doi.org/10.1016/S1571-0653(04)00576-1

**Different levels of randomness in Random Ramsey theorems.** / Simonovits, Miklós; Sós, Vera T.

Research output: Contribution to journal › Article

*Electronic Notes in Discrete Mathematics*, vol. 15, pp. 189-192. https://doi.org/10.1016/S1571-0653(04)00576-1

}

TY - JOUR

T1 - Different levels of randomness in Random Ramsey theorems

AU - Simonovits, Miklós

AU - Sós, Vera T.

PY - 2003/5

Y1 - 2003/5

N2 - Extremal graph theory, Ramsey theory and the theory of Random graphs are strongly connected to each other. Starting from these fields, we formulate some problems and results which are related to different levels of randomness. The first one is completely non-random, being the ordinary Ramsey-Turán problem and in the subsequent three problems we formulate some randomized variations of the problem. Speaking of graph properties, we shall consider them as sets of graphs and occasionally write G ∈ P instead of writing that G has property P. A graph property P is called monotone if adding an edge to a Hn ∈ P, we get an H*n ∈ P. We shall use three models of random graphs: the binomial, the hypergeometric and the stopping-rule model. This abstract contains the most important definitions.

AB - Extremal graph theory, Ramsey theory and the theory of Random graphs are strongly connected to each other. Starting from these fields, we formulate some problems and results which are related to different levels of randomness. The first one is completely non-random, being the ordinary Ramsey-Turán problem and in the subsequent three problems we formulate some randomized variations of the problem. Speaking of graph properties, we shall consider them as sets of graphs and occasionally write G ∈ P instead of writing that G has property P. A graph property P is called monotone if adding an edge to a Hn ∈ P, we get an H*n ∈ P. We shall use three models of random graphs: the binomial, the hypergeometric and the stopping-rule model. This abstract contains the most important definitions.

UR - http://www.scopus.com/inward/record.url?scp=34247133039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247133039&partnerID=8YFLogxK

U2 - 10.1016/S1571-0653(04)00576-1

DO - 10.1016/S1571-0653(04)00576-1

M3 - Article

VL - 15

SP - 189

EP - 192

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -