Some properties of graphs of diameters
type: Item
instance of: scholarly article
title: Some properties of graphs of diameters
zbMATH Open document ID: 0965.05063
published in: Discrete \& Computational Geometry
publication date: 2001-08-05T00:00:00Z
review text: The graph of diameters on a given subset \(V\) of a metric space is defined as the graph with vertices the elements of \(V\), where two vertices are adjacent if they are at distance equal to the diameter of \(V\). It is proved that any two cycles of odd order in the graph of diameters in the 3-dimensional Euclidean space have a common vertex. Some properties of such graphs in Banach spaces are also studied.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1507676
zbMATH Keywords: graph of diameters
zbMATH Keywords: metric space
zbMATH Keywords: diameter
zbMATH Keywords: cycles
zbMATH Keywords: Euclidean space
zbMATH Keywords: Banach spaces
author: Vladimir L. Dol'nikov
reviewed by: Vladimir D. Tonchev
MaRDI profile type: Publication
full work available at URL: s004540010036
OpenAlex ID: W1964607221
DOI: 10.1007/S004540010036
description: scientific article; zbMATH DE number 1507676