On induced Ramsey numbers for graphs with bounded maximum degree
type: Item
instance of: scholarly article
title: On induced Ramsey numbers for graphs with bounded maximum degree
zbMATH Open document ID: 0855.05084
author: Tomasz Łuczak
author: Vojtěch Rödl
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-01-26T00:00:00Z
review text: The induced Ramsey number \(r_{\text{ind}}(H)\) for a graph \(H\) is defined as the minimum number of vertices in a graph \(G\) which has the property that every 2-edge colouring of \(G\) yields an induced monochromatic copy of \(H\). It is shown that for every \(d\geq 1\) there exists an absolute constant \(c_d\) such that \(r_{\text{ind}}(H_{n, d})\leq n^{c_d}\) for every graph \(H_{n, d}\) with \(n\) vertices and the minimum degree at most \(d\). This confirms a conjecture suggested by W. T. Trotter.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 934798
zbMATH Keywords: Ramsey number
MaRDI profile type: Publication
full work available at URL: jctb.1996.0025
OpenAlex ID: W2037759693
DOI: 10.1006/JCTB.1996.0025
description: scientific article; zbMATH DE number 934798