Multipartite graph-sparse graph Ramsey numbers
type: Item
instance of: scholarly article
title: Multipartite graph-sparse graph Ramsey numbers
zbMATH Open document ID: 0593.05050
DOI: 10.1007/BF02579245
author: Ralph Faudree
author: Cecil Rousseau
author: R. H. Schelp
author: P. Erdős
published in: Combinatorica
publication date: 1985-01-01T00:00:00Z
review text: Let \(F\) and \(G\) be finite graphs. The Ramsey number \(r(F,G)\) is the smallest positive integer n so that, given any graph on \(n\) vertices, either it contains a subgraph isomorphic to \(F\) or its complement contains a subgraph isomorphic to \(G\). In this paper, the Ramsey number \(r(F,G)\) is determined in the case where \(F\) is an arbitrary fixed graph and \(G\) is a sufficiently large sparse connected graph with restrictions on the maximum degree of its vertices. An asymptotically correct upper bound is obtained for \(f(F,T)\) where \(T\) is a sufficiently large, but otherwise arbitrary, tree.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 3952818
zbMATH Keywords: Ramsey number
zbMATH Keywords: sufficiently large sparse connected graph
reviewed by: Jack E. Graver
MaRDI profile type: Publication
Wikidata QID: Q105941622
cites work: Ramsey numbers for cycles in graphs
cites work: Ramsey Numbers Involving Graphs with Long Suspended Paths
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cites work: Q3926614
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full work available at URL: https://doi.org/10.1007/bf02579245
OpenAlex ID: W2018470147
description: scientific article; zbMATH DE number 3952818