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**Zentralblatt MATH**

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

**Zbl.No: ** 152.41201

**Autor: ** Erdös, Pál; Hajnal, András

**Title: ** On chromatic graphs (In Hungarian)

**Source: ** Mat. Lapok 18, 1-4 (1967).

**Review: ** Authors' summary: ``A graph G is said to have property T_{c} if for every k and every k of its vertices x_{1},...,x_{k} the subgraph G(x_{1},...,x_{k}) spanned by the vertices x_{1},...,x_{k} contains a set of independent vertices having ck elements. We show that for every c < ^{1}/_{2} there is a graph G having property T_{c} and chromatic number \aleph_{0}. Clearly a graph having property T_{ ½} has chromatic number at most 2. The question is left open if for every m > \aleph_{0} and every c < ^{1}/_{2} there is a graph G having m vertices, satisfying property T_{c} and of chromatic number m.''

**Reviewer: ** Cs.Pogány

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

**Index Words: ** topology

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag