\([2,3]\)-factors in a 3-connected infinite planar graph.
type: Item
instance of: scholarly article
title: \([2,3]\)-factors in a 3-connected infinite planar graph.
zbMATH Open document ID: 1039.05025
DOI: 10.1007/BF02936203
author: Hwan-Ok Jung
published in: Journal of Applied Mathematics and Computing
publication date: 2002-01-01T00:00:00Z
review text: Let \(G = (V,E)\) be a graph. An \([m,n]\)-factor in \(G\) is a spanning subgraph \(F\) of \(G\) which satisfies the property: \(m \leq d_{F}(x) \leq n,\) for all \(x \in V(F).\) The author investigates \([m,n]\)-factors of 3-connected locally finite infinite planar graphs containing no unbounded faces. Let \(G\) be such a graph with additional conditions (i) it contains no vertex accumulation points; and (ii) \(d_{G}(v) \geq 4\) for all \(v \in V(G).\) The main result is the theorem that for every such graph there exists a \([2,3]\)-factor. This theorem extends the result by \textit{H. Enomoto, T. Iida} and \textit{K. Ota} [J. Comb. Theory, Ser. B 68, 314--323 (1996; Zbl 0861.05022)] that every 3-connected planar graph whose minimum degree is greater than or equal to 4 has a connected \([2,3]\)-factor. The organization of the paper is as follows: 1. Introduction. 2. Preliminary results. 3. Factors in a bridge. 4. Suitable factors and proof of the main theorem. In concluding remarks the author formulates the conjecture that every 3-connected locally finite infinite planar graph satisfying \(d_{G}(v) \geq 4\) for all \(v \in V(G)\) contains a \([2,3]\)-factor.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1836013
zbMATH Keywords: spanning subgraphs
zbMATH Keywords: infinite graphs
reviewed by: Nikolaj M. Glazunov
MaRDI profile type: Publication
cites work: Trees in Polyhedral Graphs
cites work: Q3097395
cites work: Q4894619
cites work: Connected spanning subgraphs of 3-connected planar graphs
cites work: 2‐connected coverings of bounded degree in 3‐connected graphs
cites work: 2-walks in circuit graphs
cites work: Q4014627
cites work: One-way infinite Hamiltonian paths in infinite maximal planar graphs
cites work: Q4954673
cites work: Q4224438
cites work: Planarity and duality of finite and infinite graphs
full work available at URL: https://doi.org/10.1007/bf02936203
OpenAlex ID: W2008523834
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description: scientific article; zbMATH DE number 1836013