A short proof of Halin's grid theorem
type: Item
instance of: scholarly article
title: A short proof of Halin's grid theorem
zbMATH Open document ID: 1062.05138
DOI: 10.1007/BF02941538
author: Reinhard Diestel
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2005-02-28T00:00:00Z
review text: An end of an infinite graph is an equivalence class of rays (1-way infinite paths), where two rays are equivalent if no finite set of vertices separates them. An end is thick if there are infinitely many disjoint rays all converging to that end. In the paper there is a short proof of a theorem by Halin, which states that whenever a graph has a thick end, it has a subgraph isomorphic to a subdivision of a hexagonal grid \(H\) whose rays all belong to that end.
reviewed by: Martin Knor
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C83
zbMATH DE Number: 2139436
zbMATH Keywords: hexagonal grid
zbMATH Keywords: infinite graph
zbMATH Keywords: ray
zbMATH Keywords: thick end
MaRDI profile type: Publication
cites work: Q4507228
cites work: Graph-theoretical versus topological ends of graphs.
cites work: Über unendliche Wege in Graphen
cites work: Über die Maximalzahl fremder unendlicher Wege in Graphen
description: scientific article; zbMATH DE number 2139436