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Spanning trees of locally finite graphs. (English) Zbl 0679.05023
Let \(P,P_ 0,P_ 1,..\). denote one-way infinite paths in a connected locally-finite infinite graph G. Two such paths \(P_ 1\) and \(P_ 2\) are equivalent if there exists a path \(P_ 0\) such that if P is any one-way infinite subgraph of \(P_ 0\) then P has vertices in common with both \(P_ 1\) and \(P_ 2\). Classes of equivalent paths are called ends and an end E is called free if there exists a finite set R of vertices such that G-R has a connected component that contains one-way infinite paths from E but none from any other ends of G. Let E denote a free end of G. The author proves various results on the existence of a spanning tree T of G having a specified number of ends belonging to E.
Reviewer: J.W.Moon

MSC:
05C05 Trees
05C38 Paths and cycles
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References:
[1] Halin R.: Über unendliche Wege in Graphen. Math. Annalen 157 (1964), 125-137. · Zbl 0125.11701
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