## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  231.05110
Autor:  Erdös, Pál
Title:  On the graph-theorem of Pál Turán. (In Hungarian)
Source:  Mat. Lapok 21 (1970), 249-251 (1971).
Review:  Let Gn be a graph of n vertices, x1, ... ,xn. Assume v(x1) \geq v(x2) \geq ... \geq v(xn) where v(x) is the valency of the vertex x. Assume that Gn does not contain a complete subgraph of r vertices. The author proves that there is a graph G'n having chromatic number r-1 for which v(yi) \geq v(xi), i = 1, ... ,n (y1, ... ,yn are the vertices of Gn). The method is essentially identical with that of B. Andrásfai [Publ. Math. Inst. Hung. Acad. Sci., Ser. A 7, 193-196 (1962; Zbl 114.40001)].
Classif.:  * 05C15 Chromatic theory of graphs and maps

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