On the tangle compactification of infinite graphs

TL;DR

This paper explores the tangle compactification of infinite graphs, extending the concept of ends compactification from locally finite graphs to all infinite graphs, providing a new topological perspective.

Contribution

It introduces and investigates the tangle compactification for arbitrary infinite graphs, generalizing the classical ends compactification.

Findings

Tangle compactification extends the Freudenthal compactification to all infinite graphs.

Provides a new topological framework for understanding connectivity in infinite graphs.

Establishes properties and potential applications of the tangle compactification.

Abstract

In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs. Thus, the arising tangle compactification extends the well-known Freudenthal compactification from connected locally finite graphs to arbitrary infinite graphs. This Master's thesis investigates the tangle compactifcation.