Quickly proving Diestel's normal spanning tree criterion
Max Pitz
TL;DR
This paper provides two concise proofs of Diestel's criterion, establishing that a connected graph has a normal spanning tree if it lacks a specific complex subdivision involving uncountably many parallel edges.
Contribution
The paper introduces two simplified proofs of Diestel's normal spanning tree criterion, enhancing understanding and accessibility of this graph theory result.
Findings
Two short proofs of Diestel's criterion are presented.
The criterion applies to graphs without certain complex subdivisions.
The proofs simplify the understanding of conditions for normal spanning trees.
Abstract
We present two short proofs for Diestel's criterion that a connected graph has a normal spanning tree provided it contains no subdivision of a countable clique in which every edge has been replaced by uncountably many parallel edges.
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