Constructing tree-decompositions that display all topological ends

TL;DR

This paper provides a concise topological proof demonstrating that every graph has a tree-decomposition capable of displaying all its topological ends, enhancing understanding of graph structure.

Contribution

It introduces a new topological proof technique to construct tree-decompositions that display all topological ends of graphs.

Findings

All graphs admit such tree-decompositions.

The proof is notably short and topological in nature.

Abstract

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.