On Ramsey graphs without bipartite subgraphs
type: Item
instance of: scholarly article
title: On Ramsey graphs without bipartite subgraphs
zbMATH Open document ID: 0766.05057
DOI: 10.1016/0012-365X(92)90605-F
author: J. Nešetřil
author: Vojtěch Rödl
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Let \(G\) and \(H\) be graphs; the autors write \(G\to(H)\) to indicate that, given any 2-coloring of the edges of \(G\), there exists a monochromatic subgraph \(G\) isomorphic to \(H\). The main result of this paper is: Theorem 4. Let \(m,n\leq 2\) be positive integers. Then for every triangle- free graph \(H\) without \(K_{m,n}\) there exists a triangle-free graph \(G\) without \(K_{m,n}\) so that \(G\to(H)\). If \(H\) is bipartite, then \(G\) may be chosen to be bipartite.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 89905
zbMATH Keywords: Ramsey graphs
zbMATH Keywords: bipartite graphs
zbMATH Keywords: triangle-free graph
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring
cites work: Q3903002
cites work: The Ramsey property for graphs with forbidden complete subgraphs
cites work: Q3859789
cites work: Strong Ramsey Theorems for Steiner Systems
cites work: Simple proof of the existence of restricted Ramsey graphs by means of a partite construction
full work available at URL: 0012-365x(92)90605-f
OpenAlex ID: W2080652794
description: scientific article; zbMATH DE number 89905