Locally Ramsey properties of graphs
type: Item
instance of: scholarly article
title: Locally Ramsey properties of graphs
zbMATH Open document ID: 0665.05032
DOI: 10.1007/BF01139574
author: S. G. Sal'nikov
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: A graph G is local relative to a given k-vertex graph \(H_ k\) if any k vertices of G span a graph that contains \(H_ k\). The local Ramsey number \(R=LR(H_ k,m)\) is the least integer R such that any graph G on R vertices either contains a clique on m vertices or is not local relative to \(H_ k\). Thus, clearly \(LR(H_ k',m)\geq LR(H_ k,m)\) if \(H_ k'\) is a subgraph of \(H_ k\). Local Ramsey numbers for special classes of graphs are determined. For example, the following is proved. Theorem: If \(H_ k\) contains a spanning star as a subgraph and the complement of \(H_ k\) does not contain a perfect matching, then \(LR(H_ k,m)=k- cl(H_ k)+\max \{m,cl(H_ k)\}\), where cl represents the clique number of a graph. Other special graphs considered are those obtained from complete graphs by deleting spanning cycles or paths. Other functions related to the local Ramsey number LR are also considered and results for specific families of graphs are obtained.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 4087700
zbMATH Keywords: local properties
zbMATH Keywords: local Ramsey number
MaRDI profile type: Publication
cites work: Q3907600
cites work: Q3916601
cites work: Q3947696
cites work: More results on Ramsey-Turán type problems
cites work: Q3718743
Recommended article: Local Ramsey numbers for some graphs
Recommended article: Local Anti-Ramsey Numbers of Graphs
Recommended article: Local and Mean Ramsey Numbers for Some Graphs
Recommended article: Ramsey numbers for local colorings
Recommended article: Ramseyan properties of graphs
Recommended article: Q3312281
Recommended article: Local and meank-Ramsey numbers for complete graphs
Recommended article: Local Ramsey numbers for copies of cycles
Recommended article: Q5392245
description: scientific article; zbMATH DE number 4087700