Ends in spanning trees
The author deals with infinite graphs. R. Halin defined an end \(E\) of an infinite graph \(G\) as a set of 1-way infinite paths in \(G\) such that vertices \(P\) and \(Q\) are in \(E\) iff for any subset \(R\) of the vertice set there is a finite path in \(G-R\) joining \(P\) and \(Q\). The author proves that if \(T\) is a locally finite spanning tree of a connected infinite graph \(G\) and \(E\) is an end of \(G\), then \(T\) has at least one 1-way infinite path in \(E\).
scientific article; zbMATH DE number 89966
scientific article