Edge-coloring cliques with three colors on all 4-cliques
type: Item
instance of: scholarly article
title: Edge-coloring cliques with three colors on all 4-cliques
zbMATH Open document ID: 0910.05035
DOI: 10.1007/PL00009822
author: Dhruv Mubayi
published in: Combinatorica
publication date: 1999-03-14T00:00:00Z
review text: For integers \(n,p\) and \(q\), a \((p,q)\)-coloring of \(K_n\) is a coloring of the edges of \(K_n\) in which the edges of every \(p\)-cligue together receive at least \(q\) colors. Let \(f(n,p,q)\) denote the minimum number of colors in a \((p,q)\)-coloring of \(K_n\). The author proves that \(f(n,4,3)<\exp(\sqrt{c\log n}(1+O(1)))\), where \(c=4\log 2\). This improves the corresponding result by \textit{P. Erdős} and \textit{A. Gyárfás} [A variant of the classical Ramsey problem, Combinatorica 17, No. 4, 459-467 (1997; Zbl 0910.05034)].
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 1261230
zbMATH Keywords: generalized Ramsey
zbMATH Keywords: Ramsey theory
zbMATH Keywords: coloring
zbMATH Keywords: bounds
reviewed by: G. Gutin
MaRDI profile type: Publication
full work available at URL: pl00009822
OpenAlex ID: W2091175510
description: scientific article; zbMATH DE number 1261230