A conjecture concerning Ramsey's theorem
type: Item
instance of: scholarly article
title: A conjecture concerning Ramsey's theorem
zbMATH Open document ID: 0790.05058
DOI: 10.1016/0012-365X(94)90284-4
published in: Discrete Mathematics
publication date: 1994-04-04T00:00:00Z
review text: An exact \(c\)-coloring of the edges of a graph is defined to be one in which all \(c\) colors are used. Ramsey's Theorem is generalized accordingly: let \(P(c,m)\) be the statement that every exact \(c\)-coloring of the edges of a countable infinite complete graph yields an exactly \(m\)-colored infinite complete subgraph. It is inquired as to which ordered pairs \((c,m)\) make \(P(c,m)\) true. Sufficient conditions are found, and it is conjectured that these conditions are necessary. Constructions show that this is true for a density 1 of ordered pairs \((c,m)\).
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 540956
zbMATH Keywords: exact \(c\)-coloring
zbMATH Keywords: Ramsey's Theorem
Wikidata QID: Q122924459
author: Martin J. Erickson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 540956