## 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 fk(x), 1 \leq k \leq n, n > 2\nu be continuous functions in [0,1] satisfying fk(0) = 0, |fk(t1)-fk(t2)| \leq |t1-t2| for 0 \leq t1 < t2 \leq 1. Then there are at least n2/2\nu -n/2 pairs i \ne j so that max0 \leq t \leq 1 |fi(x)-fj(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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