Binomial coefficients and zero-sum Ramsey numbers
type: Item
instance of: scholarly article
title: Binomial coefficients and zero-sum Ramsey numbers
zbMATH Open document ID: 0883.05101
author: Yair Caro
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-02-22T00:00:00Z
review text: Let \(H\) be a \(k\)-uniform hypergraph and \(G\) be an abelian group. The zero-sum Ramsey number \(R(H,G)\) is the least integer \(n\) such that if the edges of the complete \(k\)-uniform hypergraph \(K_n^k\) are \(G\)-colored, then there is a zero-sum (mod \(G\)) copy of \(H\) in \(K_n^k\). It is shown that the Ramsey number \(R(K_n,Z_p) \leq n + 2p - 2\), and for \(k \geq 2\), \(R(K_n^k,Z_2) \leq n + k\). Precise values of the Ramsey number for some special cases are determined.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 1093113
zbMATH Keywords: zero-sum
zbMATH Keywords: edge coloring
zbMATH Keywords: abelian group
zbMATH Keywords: Ramsey numbers
reviewed by: Ralph Faudree
MaRDI profile type: Publication
full work available at URL: jcta.1997.2812
OpenAlex ID: W2037207916
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DOI: 10.1006/JCTA.1997.2812
description: scientific article; zbMATH DE number 1093113