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**Zentralblatt MATH**

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

**Zbl.No: ** 232.05003

**Autor: ** Erdös, Paul; Meir, A.; Sós, V.T.; Turán, P.

**Title: ** On some applications of graph theory. III. (In English)

**Source: ** Can. Math. Bull. 15, 27-32 (1972).

**Review: ** The results of our first paper are generalized for metric spaces. As an application we prove among others the following theorem: Let f_{k}(x), 1 \leq k \leq n, n > 2^{\nu} be continuous functions in [0,1] satisfying f_{k}(0) = 0, |f_{k}(t_{1})-f_{k}(t_{2})| \leq |t_{1}-t_{2}| for 0 \leq t_{1} < t_{2} \leq 1. Then there are at least n^{2}/2^{\nu} -n/2 pairs i \ne j so that **max**_{0 \leq t \leq 1} |f_{i}(x)-f_{j}(x)| \leq {2 \over \nu}. The theorem is best possible. [Our first paper will appear in Discrete Math.; for the second see Studies pure Math., Papers presented to Richard Rado on the Occasion of his sixty fifth Birthday, 89-99 (1971; Zbl 218.52005)].

**Classif.: ** * 05C90 Appl. of graph theory

05C99 Graph theory

**Citations: ** Zbl 245.05130; Zbl 236.05119; Zbl 218.323

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