An application of Lovász' local lemma‐A new lower bound for the van der Waerden number

Authors:
Zoltán Szabó
Affiliations:
Eötvös Lóránd University Budapest, Balzac U.18, 1136 Hungary
Venue:
Random Structures & Algorithms
Year:
1990

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Abstract

The van der Waerden number W(n) is the smallest integer so that if we divide the integers {1,2, …, W(n)} into two classes, then at least one of them contains an arithmetic progression of length n. We prove in this paper that W(n) ≥ 2n/nϵ for all sufficiently large n. © 1990 Wiley Periodicals, Inc.