Remarks on the size Ramsey number of graphs
type: Item
instance of: scholarly article
title: Remarks on the size Ramsey number of graphs
zbMATH Open document ID: 0617.05049
DOI: 10.1007/BF01849031
author: Halina Bielak
published in: Periodica Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: Let G denote a finite graph with vertex set V(G) and edge set E(G). If F is a second graph, we write \(G\to F\) to denote that, for every 2-coloring of the edges of G, G contains a monochromatic copy of F. The author defines: \(r(F)=\min \{| V(G)|: G\to F\},\) which one easily sees is the usual Ramsey number r(F,F). This formulation of the definition leads one to define the size Ramsey number: \(\hat r(F)=\min \{| E(G)|: G\to F\}.\) This paper contains several results concerning the size Ramsey number for special graphs. For example: \(\hat r(P_ 3)=7\), \(\hat r(P_ 4)\leq 11\); where \(P_ i\) is the path of length i.
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 3999976
zbMATH Keywords: Ramsey number
zbMATH Keywords: size Ramsey number
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: On size Ramsey number of paths, trees, and circuits. I
cites work: Q3972752
cites work: The size Ramsey number
cites work: Size Ramsey numbers involving stars
cites work: Size Ramsey numbers for small‐order graphs
full work available at URL: https://doi.org/10.1007/bf01849031
OpenAlex ID: W1978156707
description: scientific article; zbMATH DE number 3999976