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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 242.05122

**Autor: ** Erdös, Paul; Szemeredi, A.

**Title: ** On a Ramsey type theorem. (In English)

**Source: ** Period. Math. Hung. 2, 295-299 (1972).

**Review: ** Let \bar G denote the complement of the graph G, and let K_{n} denote the complete graph on n vertices. The main result of this paper is the following theorem: Theorem 2. Let G(n,r) be a graph of n vertices with r < {n^{2} \over k} edges. Then there is a positive constant c such that for s < c{k \over log k} log n, either \overline{G(n,r)} or G(n,r) contains K_{s} as a subgraph. This result is shown to be best possible as far as the order of magnitude is concerned.

**Reviewer: ** J.E.Graver

**Classif.: ** * 05C15 Chromatic theory of graphs and maps

05C35 Extremal problems (graph theory)

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