A simple existence criterion for normal spanning trees in infinite graphs

Abstract

Halin proved in 1978 that there exists a normal spanning tree in every connected graph $G$ that satisfies the following two conditions: (i) $G$ contains no subdivision of a `fat' $K_{{\aleph }_0}$, one in which every edge has been replaced by uncountably many parallel edges; and (ii) $G$ has no $K_{{\aleph }_0}$ subgraph. We show that the second condition is unnecessary.

Reader guidance in proof of Lemma 5 rewritten; no changes in substance

References in corpus (1)

• Locally finite graphs with ends: a topological approach