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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