Edge-Ramsey theory
type: Item
instance of: scholarly article
title: Edge-Ramsey theory
zbMATH Open document ID: 0849.05065
DOI: 10.1007/BF02711499
author: Yanyan Li
published in: Discrete \& Computational Geometry
publication date: 1996-11-05T00:00:00Z
review text: Let \((K_n, E_n)\) be a sequence of graphs in Euclidean spaces \(\mathbb{R}^n\). It is said to be edge-Ramsey if, for all \(r\geq 1\), a positive integer \(n= n(K, E, r)\) exists so that if \(m\geq n\), for any \(r\)-coloring of the edges of \(\mathbb{R}^m\), there is a graph \((L, F)\) in \(\mathbb{R}^m\) which is geometrically congruent to \((K_m, E_m)\) so that all edges in \(F\) are assigned the same color. It is shown that the graphs of the \(n\)-dimensional measure polytope (the \(n\)-cube) and of the \(n\)-dimensional cross polytope are edge-Ramsey. Together with the \(n\)-dimensional simplices these are the only regular edge-Ramsey polytopes, with the possible exceptions of the hexagon and the 24-cell.
reviewed by: Konrad Engel
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 52C10
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 881219
zbMATH Keywords: Euclidean-Ramsey theory
zbMATH Keywords: edge-configuration
zbMATH Keywords: edge-Ramsey
zbMATH Keywords: measure polytope
zbMATH Keywords: cross polytope
zbMATH Keywords: edge-Ramsey polytopes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 881219