Menger's theorem for countable graphs
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 \({\mathcal P}\).
scientific article; zbMATH DE number 4025475