On four color monochromatic sets with nondecreasing diameter
type: Item
instance of: scholarly article
title: On four color monochromatic sets with nondecreasing diameter
zbMATH Open document ID: 1074.05087
author: David J. Grynkiewicz
published in: Discrete Mathematics
publication date: 2005-04-18T00:00:00Z
review text: The author investigates a generalized Ramsey question. The function \(f(n,k)\) denotes the smallest integer \(M\) such that for every \(k-\)coloring of positive integers not exceeding \(M\), there exist two monochromatic sets \(X_1,X_2\subseteq [1,M]\), \(| X_1| =| X_2| =n,\) and the condition \(\max(X_1)<\min(X_2)\) holds. It is proved that \(f(n,4)\leq 12n-9.\) Since a classical result of Erdős, Ginzburg and Ziv implies \(f(n,4)\geq 12n-9,\) this bound is sharp. The determination of the function \(f(n,k)\) is related to a generalization of a zero-sum problem.
reviewed by: Norbert Hegyvári
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 2157729
zbMATH Keywords: Ramsey theory
zbMATH Keywords: zero-sum problems
MaRDI profile type: Publication
full work available at URL: j.disc.2004.10.010
OpenAlex ID: W1987161111
cites work: Ascending waves
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DOI: 10.1016/J.DISC.2004.10.010
description: scientific article; zbMATH DE number 2157729