Separating double rays in locally finite planar graphs
type: Item
instance of: scholarly article
title: Separating double rays in locally finite planar graphs
zbMATH Open document ID: 0843.05021
DOI: 10.1016/0012-365X(94)00054-M
author: C. Paul Bonnington
author: Wilfried Imrich
author: Mark E. Watkins
published in: Discrete Mathematics
publication date: 1996-08-13T00:00:00Z
review text: The authors consider locally finite, 1-ended graphs \(\Gamma\) such that the automorphism group of \(\Gamma\) acts with finitely many orbits on \(V(\Gamma)\). They first show that if \(\Gamma\) is 3-connected and planar, then for each double ray \(D\) in \(\Gamma\) the graph \(\Gamma- V(D)\) has at most two infinite components and exactly two, if in addition \(D\) is a quasi-axis (i.e. \(\text{dist}_D(x, y)\leq \text{Sdist}_\Gamma(x, y)\) for some constant S and all \(x, y\in V(D)\)). Adapting a method of \textit{C. Thomassen} [The Hadwiger number of infinite vertex-transitive graphs, Combinatorica 12, No. 4, 481-491 (1992; Zbl 0776.05053)] they prove that conversely almost 4-connected \(\Gamma\) are planar if for each quasi-axis \(D\) the graph \(\Gamma- V(D)\) has exactly two infinite components.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 810255
zbMATH Keywords: planar graphs
zbMATH Keywords: automorphism group
zbMATH Keywords: double ray
zbMATH Keywords: components
zbMATH Keywords: quasi-axis
reviewed by: Heinz A. Jung
MaRDI profile type: Publication
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cites work: Automorphisms and endomorphisms of infinite locally finite graphs
cites work: Q4094882
cites work: A note on fragments of infinite graphs
cites work: On the connectivities of finite and infinite graphs
cites work: 2-linked graphs
cites work: Duality of infinite graphs
cites work: The Hadwiger number of infinite vertex-transitive graphs
cites work: Infinite paths that contain only shortest paths
full work available at URL: 0012-365x(94)00054-m
OpenAlex ID: W1970209184
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description: scientific article; zbMATH DE number 810255