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**Zentralblatt MATH**

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

**Zbl.No: ** 117.17402

**Autor: ** Erdös, Pál

**Title: ** On a problem in graph theory (In English)

**Source: ** Math. Gaz. 47, 220-223 (1963).

**Review: ** Let f(k) be the minimum number of vertices in a complete graph which can be so oriented that, for every set S of k vertices, there is a vertex x joined to all elements of S by edges directed from x to S. The author proves that f(k) \geq 2^{k+1}-1 and **limsup** 2^{-k} k^{-2} f(k) \leq log 2.

**Reviewer: ** C.St.J.A.Nash-Williams

**Classif.: ** * 05C35 Extremal problems (graph theory)

**Index Words: ** topology

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