The structure of rayless graphs
type: Item
instance of: scholarly article
title: The structure of rayless graphs
zbMATH Open document ID: 0946.05070
DOI: 10.1007/BF02942564
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2000-03-19T00:00:00Z
review text: A ray is a one-way infinite path. The author first presents the main concepts in investigating rayless graphs, called order and kernel, developed by \textit{R. Schmidt} [Ein Reduktionsverfahren für weg-endliche Graphen, Dissertation, Univ. Hamburg (1982; Zbl 0526.05059); see also: Ein Ordnungsbegriff für Graphen ohne unendliche Wege mit Anwendungen auf \(n\)-fach zusammenhängende Graphen, Arch. Math. 40, 283-288 (1983; Zbl 0526.05058)]. The author then investigates the relationship between order and kernel and tree-decompositons, and finally generalizes an interesting theorem of \textit{N. Polat} and \textit{G. Sabidussi} [Fixed elements of infinite trees, Discrete Math. 130, No. 1-3, 97-102 (1994; Zbl 0817.05065)], saying that in every rayless tree there is a vertex or an edge left fixed by every automorphism of the tree to connected rayless graphs.
reviewed by: Van Bang Le
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1416675
zbMATH Keywords: infinite graph
zbMATH Keywords: rayless graph
zbMATH Keywords: tree-decompositon
zbMATH Keywords: endomorphism of graphs
author: Rudolf Halin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1416675