Publications of (and about) Paul Erdös
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 n1 < n2 < ··· 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 n1 < n2 < ··· such that nk < (1+o(1))k2/2 for infinitely many k.
Classif.: * 05C55 Generalized Ramsey theory
Index Words: topology
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