The ith Ramsey number for matchings
type: Item
instance of: scholarly article
title: The ith Ramsey number for matchings
zbMATH Open document ID: 0602.05048
DOI: 10.1016/0012-365X(86)90034-8
author: R. Glenn Powers
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Given graphs \(G_ 1,...,G_ k\) we denote by \(r_ i(G_ 1,...,G_ k)\) the least integer p so that, if the complete p-partite graph K(i,...,i) with each vertex set of size i has its edges colored with k colors, \(c_ 1,...,c_ k\), then, for some index j, there is a subgraph of K(i,...,i) isomorphic to \(G_ j\) with all of its edges colored \(c_ j\). One easily checks that the usual Ramsey number associated with \(G_ 1,...,G_ k\) is, in this notation, \(r_ 1(G_ 1,...,G_ k)\). The Ramsey index for \(G_ 1,...,G_ k\) is defined to be the least index i such that \[ r_ i(G_ 1,...,G_ k)=\lim_{j\to \infty}(G_ 1,...,G_ k); \] and is denoted by \(i(G_ 1,...,G_ k)\). The main results of this paper include: Theorem 9. Let \(k,m_ 1,...,m_ k\) be positive integers, then \[ i(m_ 1K_ 2,...,m_ kK_ 2) = \sum^{k}_{j=1}(m_ j-1)+1. \]
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 3970797
zbMATH Keywords: Ramsey number
zbMATH Keywords: Ramsey index
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: Q4187840
cites work: Q3922716
cites work: Q4100121
cites work: Q4044600
cites work: The Ramsey number for stripes
cites work: Path-path Ramsey type numbers for the complete bipartite graph
description: scientific article; zbMATH DE number 3970797