Bounds on Ramsey numbers of certain complete bipartite graphs
type: Item
instance of: scholarly article
title: Bounds on Ramsey numbers of certain complete bipartite graphs
zbMATH Open document ID: 1009.05100
DOI: 10.1007/BF03322761
author: Roland Lortz
author: Ingrid Mengersen
published in: Results in Mathematics
publication date: 2002-08-06T00:00:00Z
review text: The authors study the two-color Ramsey numbers \(r(K_{l,m}, K_{l,n})\) for \(l\in\{ 3,4,5\}\), and \(m\approx n\), and for \(l=3\), \(m\) fixed, and \(n\) large. In the diagonal case, they improve the old upper bound on \(r(K_{l,n}, K_{l,n})\) from \textit{F. R. K. Chung} and \textit{R. L. Graham} [J. Comb. Theory, Ser. B 18, 164-169 (1975; Zbl 0298.05122)] for \(l\in\{ 3,4,5\}\), obtaining \(r(K_{3,n}, K_{3,n})\leq 8n -2\), \(r(K_{4,n}, K_{4,n})\leq 16n -2\), \(r(K_{5,n}, K_{5,n})\leq 32n -2\) for \(n\geq 9\), as well as some lower bounds, and some similar bounds for the off-diagonal cases.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 1760648
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: complete bipartite graphs
reviewed by: Peter Brass
MaRDI profile type: Publication
cites work: On multicolor Ramsey numbers for complete bipartite graphs
cites work: Q3976617
cites work: Q4873742
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cites work: Off‐diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)
cites work: Combinatorics. Room squares, sum-free sets, Hadamard matrices
description: scientific article; zbMATH DE number 1760648