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**Zentralblatt MATH**

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

**Zbl.No: ** 346.05106

**Autor: ** Erdös, Paul; Preiss, D.

**Title: ** Decomposition of spheres in Hilbert spaces. (In English)

**Source: ** Commentat. Math. Univ. Carol. 17, 791-795 (1976).

**Review: ** We join two points of the unit sphere of the Hilbert space of __X___{\alpha+2} dimension by edge if their distance is greater than 3/2. By using the generalized continuum hypothesis there is proved that the chromatic number of this graph is __X___{\alpha+1} and that every subgraph spanned by __X___{\alpha+1} vertices has chromatic number \leq __X___{\alpha}.

**Reviewer: ** J.Fiamcik

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

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