On the Ramsey problem for multicolor bipartite graphs
type: Item
instance of: scholarly article
title: On the Ramsey problem for multicolor bipartite graphs
zbMATH Open document ID: 0916.05052
published in: Advances in Applied Mathematics
publication date: 1999-02-02T00:00:00Z
review text: Given positive integers \(i,j\), let \(K_{i,j}\) denote a bipartite complete graph and let \(R_r(m,n)\) be the smallest integer \(a\) such that for any \(r\)-colouring of the edges of \(K_{a,a}\) one can always find a monochromatic subgraph isomorphic to \(K_{m,n}\). It is shown that \(R_2(m,n)\leq 2^m (n-1)+ 2^{m-1}-1\), which generalizes the results for \(m=2, 3\) due to Beineke and Schwenk. Moreover, a class of lower bounds based on properties of orthogonal Latin squares is found which establishes that \(\lim_{r\to \infty}R_r(2,2) r^{-2}=1\).
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 1247941
zbMATH Keywords: Ramsey problem
author: Walter Carnielli
author: Emerson L. Monte Carmelo
reviewed by: Chris Jagger
MaRDI profile type: Publication
full work available at URL: aama.1998.0620
OpenAlex ID: W1987259761
cites work: In Memoriam: Paul Erdős 1913–1996
cites work: Q4100119
cites work: Q3737429
cites work: Q3852212
cites work: Hyper-rook Domain Inequalities
cites work: Some results on polarized partion relations of higher dimension
cites work: On multicolor Ramsey numbers for complete bipartite graphs
cites work: An Upper Bound on Zarankiewicz' Problem
cites work: Q3770573
cites work: Q3903002
cites work: Q5579515
cites work: Regularity and Positional Games
cites work: A new result on the problem of Zarankiewicz
cites work: A bipartite Ramsey problem and the Zarankiewicz numbers
cites work: Maximum distance&lt;tex&gt;q&lt;/tex&gt;-nary codes
DOI: 10.1006/AAMA.1998.0620
description: scientific article; zbMATH DE number 1247941