# A sufficient condition for Hamiltonicity in locally finite graphs

## TL;DR

This paper extends a finite graph Hamiltonicity result to locally finite graphs using topological circles, providing a new sufficient condition for Hamiltonicity in infinite graph settings.

## Contribution

It introduces a topological approach to characterize Hamiltonicity in locally finite graphs, answering an open question and generalizing finite graph results.

## Key findings

- Provides a sufficient condition for Hamiltonicity in locally finite graphs.
- Uses topological circles in the Freudenthal compactification to identify Hamiltonian cycles.
- Extends finite graph theory results to infinite graphs.

## Abstract

Using topological circles in the Freudenthal compactification of a graph as infinite cycles, we extend to locally finite graphs a result of Oberly and Sumner on the Hamiltonicity of finite graphs. This answers a question of Stein, and gives a sufficient condition for Hamiltonicity in locally finite graphs.