A tree-of-tangles theorem for infinite tangles

TL;DR

This paper extends the tree-of-tangles theorem to all infinite graphs, providing new insights into their topology, end spaces, and compactifications, thereby broadening the applicability of this fundamental graph theory result.

Contribution

It generalizes Carmesin's extension of the theorem to all infinite graphs, advancing the understanding of their structural and topological properties.

Findings

Extended the tree-of-tangles theorem to all infinite graphs

Provided new applications for the topology of infinite graphs

Enhanced understanding of end spaces and compactifications

Abstract

Carmesin has extended Robertson and Seymour's tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications.