## 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 Kn 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 < {n2 \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 Ks 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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