Contractible edges in 2-connected locally finite graphs
type: Item
instance of: scholarly article
title: Contractible edges in 2-connected locally finite graphs
zbMATH Open document ID: 1327.05180
author: Tsz Lung Chan
published in: The Electronic Journal of Combinatorics
publication date: 2015-08-26T00:00:00Z
full work available at URL: v22i2p47
review text: Summary: In this paper, we prove that every contraction-critical 2-connected infinite graph has no vertex of finite degree and contains uncountably many ends. Then, by investigating the distribution of contractible edges in a 2-connected locally finite infinite graph \(G\), we show that the closure of the subgraph induced by all the contractible edges in the Freudenthal compactification of \(G\) is 2-arc-connected. Finally, we characterize all 2-connected locally finite outerplanar graphs nonisomorphic to \(K_3\) as precisely those graphs such that every vertex is incident to exactly two contractible edges as well as those graphs such that every finite bond contains exactly two contractible edges.
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C63
zbMATH DE Number: 6475721
zbMATH Keywords: contractible edge
zbMATH Keywords: Hamilton cycle
zbMATH Keywords: outerplanar
zbMATH Keywords: infinite graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6475721