## 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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