##
**Zentralblatt MATH**

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

**Zbl.No: ** 129.40101

**Autor: ** Erdös, Pál

**Title: ** Some remarks on Ramsay's theorem (In English)

**Source: ** Can. Math. Bull. 7, 619-622 (1964).

**Review: ** Let G be a graph whose vertices are the integers. If G contains no infinite complete subgraph then according to *Ramsey*'s theorem [Proc. London math. Soc. 30, 264-286 (1929)] it contains an infinite set of independent vertices; it cannot be asserted that the vertices n_{1} < n_{2} < ··· of such an independent set do not tend to infinity too rapidly. However, it is shown that if G contains no triangles, then there exists an infinite set of independent vertices n_{1} < n_{2} < ··· such that n_{k} < (1+o(1))k^{2}/2 for infinitely many k.

**Reviewer: ** J.W.Moon

**Classif.: ** * 05C55 Generalized Ramsey theory

**Index Words: ** topology

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag