An upper bound for Ramsey numbers.
type: Item
instance of: scholarly article
title: An upper bound for Ramsey numbers.
zbMATH Open document ID: 1057.05059
DOI: 10.1016/S0893-9659(04)90099-7
author: Yusheng Li
author: Wenan Zang
author: Cecil Rousseau
published in: Applied Mathematics Letters
publication date: 2005-02-25T00:00:00Z
review text: The Ramsey number, \(r(G,H)\) of the graphs \(G\) and \(H\) is the smallest integer \(N\) such that every colouring of the edges of \(K_N\) with red and blue yields either a red \(G\) or a blue \(H\). The Erdős-Szekeres recursion theorem yields \(r(G,H)\leq r(G',H)+r(G,H')\), where \(G'\) is a graph obtained by deleting one vertex from \(G\). This paper goes one step further, and works with \(G''\) and \(H''\), where two vertices have been deleted. Let \(A=r(G'',H)\) and \(B=r(G,H'')\), then the result is: \(r(G,H)\leq A+B+2+2\sqrt{(A^2+AB+B^2)/3}\).
reviewed by: Sheila Oates-Williams
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 2138638
zbMATH Keywords: Ramsey theory for graphs
MaRDI profile type: Publication
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full work available at URL: s0893-9659(04)90099-7
OpenAlex ID: W2057634608
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description: scientific article; zbMATH DE number 2138638