A simple existence criterion for normal spanning trees in infinite graphs

Reinhard Diestel

A simple existence criterion for normal spanning trees in infinite graphs

Combinatorics 2016-04-12 v2

Authors: Reinhard Diestel

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the following two conditions: (i) $G$ contains no subdivision of a `fat' $K_{\aleph_0}$ , one in which every edge has been replaced by uncountably many parallel edges; and (ii) $G$ has no $K_{\aleph_0}$ subgraph.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.

Keywords

spanning trees graph theory

Cite

@article{arxiv.1202.4399,
  title  = {A simple existence criterion for normal spanning trees in infinite graphs},
  author = {Reinhard Diestel},
  journal= {arXiv preprint arXiv:1202.4399},
  year   = {2016}
}

Comments

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

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