Menger's theorem for countable graphs
type: Item
instance of: scholarly article
title: Menger's theorem for countable graphs
zbMATH Open document ID: 0631.05032
DOI: 10.1016/0095-8956(87)90006-2
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: Let be G a graph with V(G) countable and A,B\(\subseteq V(G)\). The author defines a relation on the triple (G,A,B), e.g. a web or gammoid, using families of disjoint paths which separates A and B, called waves. Using this relation he proves the countable case of the following conjecture of Erdős [see, e.g. \textit{C. St. J. A. Nash-Williams}, J. Comb. Theory 3, 286-301 (1967; Zbl 0153.258)]. In any graph there exists a set \({\mathcal P}\) of disjoint A-B paths and an A-B separating set S, such that S consists of the choice of precisely one vertex from each path in \({\mathcal P}\).
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 4025475
zbMATH Keywords: infinite graphs
zbMATH Keywords: relation
zbMATH Keywords: disjoint paths
zbMATH Keywords: waves
zbMATH Keywords: separating set
author: Ron Aharoni
reviewed by: Michael Hager
MaRDI profile type: Publication
full work available at URL: 0095-8956(87)90006-2
OpenAlex ID: W2059748966
cites work: König's Duality Theorem for Infinite Bipartite Graphs
cites work: Menger's theorem for graphs containing no infinite paths
cites work: Q5663905
cites work: Q3292914
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cites work: Hamiltonian Lines in Products of Infinite Trees
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cites work: Über Translationen und den Satz von Menger in unendlichen Graphen
description: scientific article; zbMATH DE number 4025475