Augmentation Lemma for Halin Conjecture

TL;DR

This paper corrects a key property in the proof of a recent result on the Halin conjecture, which characterizes when infinite graphs have normal spanning trees.

Contribution

It provides a correction to the proof of a crucial property related to dominated torsos in the proof of the Halin conjecture.

Findings

Corrected a critical step in the proof of the Halin conjecture

Ensured the validity of the construction of dominated torsos

Strengthened the overall proof of the Halin conjecture

Abstract

The longstanding conjecture of Halin characterizing the existence of normal spanning trees in infinite graphs has been recently proved by Max Pitz [3]. A critical step in the proof involves the construction of dominated torsos, whose properties are essential to the overall proof. In this note, we provide a correction to the proof of a key property of this construction.