The bipartite Ramsey numbers
type: Item
instance of: scholarly article
title: The bipartite Ramsey numbers
zbMATH Open document ID: 1218.05101
author: Yongqi Sun
author: Rui Zhang
published in: The Electronic Journal of Combinatorics
publication date: 2011-06-01T00:00:00Z
full work available at URL: https://eudml.org/doc/233483
full work available at URL: v18i1p51.html
review text: Summary: Given bipartite graphs \(H_1\) and \(H_2\), the bipartite Ramsey number \(b(H_1; H_2)\) is the smallest integer \(b\) such that any subgraph \(G\) of the complete bipartite graph \(K_{b,b}\), either \(G\) contains a copy of \(H_1\) or its complement relative to \(K_{b,b}\) contains a copy of \(H_2\). It is known that \(b(K_{2,2}; K_{2,2}) = 5, b(K_{2,3}; K_{2,3}) = 9, b(K_{2,4}; K_{2,4}) = 14\) and \(b(K_{3,3}; K_{3,3}) = 17\). In this paper we study the case \(H_1\) being even cycles and \(H_2\) being \(K_{2,2}\), prove that \(b(C_6; K_{2,2}) = 5\) and \(b(C_{2m}; K_{2,2}) = m + 1\) for \(m \geq 4\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 5902981
zbMATH Keywords: bipartite graph
zbMATH Keywords: Ramsey number
zbMATH Keywords: even cycle
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5902981