Different levels of randomness in random Ramsey theorems

Simonovits, Miklós and T. Sós, Vera (2003) Different levels of randomness in random Ramsey theorems. ELECTRONIC NOTES IN DISCRETE MATHEMATICS, 15. pp. 189-192. ISSN 1571-0653

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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 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.

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