On the Helly property working as a compactness criterion on graphs
type: Item
instance of: scholarly article
title: On the Helly property working as a compactness criterion on graphs
zbMATH Open document ID: 0575.05026
DOI: 10.1016/0097-3165(85)90061-5
author: Alain Quilliot
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: Given a connected graph (X,E), denote by \(d_ G\) the distance given by the graph. Let \({\mathcal E}\) be a family of all balls, i.e. sets \(\{\) \(y\in X;d_ G(x,y)\leq p\}\), \(x\in X\), \(p\in N\). Then (X,E) is a Helly graph provided every subfamily of \({\mathcal E}\) in which every pair of balls meets has a non-trivial intersection. The automorphism group of a finite Helly graph is studied and fixed point theorem for finite Helly graphs is proved.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 3918391
zbMATH Keywords: connected graph
zbMATH Keywords: automorphism group
zbMATH Keywords: Helly graph
zbMATH Keywords: fixed point theorem
reviewed by: Marie Demlová
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90061-5
OpenAlex ID: W2000501728
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description: scientific article; zbMATH DE number 3918391