## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  822.05046
Autor:  Bialostocki, Arie; Erdös, Paul; Lefmann, Hanno
Title:  Monochromatic and zero-sum sets of nondecreasing diameter. (In English)
Source:  Discrete Math. 137, No.1-3, 19-34 (1995).
Review:  The authors consider a van der Waerden type number f(m, r), which is the minimum integer n such that for every coloring of the integers {1, 2,..., n} with r colors, there exist two monochromatic subsets B1 and B2 each with m integers such that each element of B1 is less than each element of B2 and that the diameter of B1 is less than or equal to the diameter of B2. They verify that f(m, 2) = 5m- 3, f(m, 3) = 9m- 7, 12m- 9 \leq f(m, 4) \leq 13m- 11, and asymptotically, c1 mr \leq f(m, r) \leq c2 mr log2 r. Similar questions are considered when the elements of Zm are used as colors and zero-sum sets are required.
Reviewer:  R.Faudree (Memphis)
Classif.:  * 05C55 Generalized Ramsey theory
Keywords:  van der Waerden number; coloring; monochromatic subsets; diameter; zero- sum sets

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