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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
##### Keywords:
locally finite graphs; infinite paths; spanning tree
Full Text:
##### References:
 [1] Halin R.: Über unendliche Wege in Graphen. Math. Annalen 157 (1964), 125-137. · Zbl 0125.11701
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