A simple existence criterion for normal spanning trees in infinite graphs

2012/02/20 by Reinhard Diestel, Diestel, Reinhard
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1202.4399

openalex publication_date 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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that satisfies the following two conditions: (i) G contains no subdivision of a `fat' K_ℵ0, one in which every edge has been replaced by uncountably many parallel edges; and (ii) G has no K_ℵ0 subgraph. We show that the second condition is unnecessary.

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