Hamilton circles in Cayley graphs

TL;DR

This paper establishes a sufficient condition for the existence of Hamilton circles in locally finite Cayley graphs, extending the concept of Hamilton cycles to infinite graphs using topological methods.

Contribution

It introduces a new criterion for Hamilton circles in Cayley graphs, broadening understanding of infinite graph Hamiltonicity.

Findings

Provides a sufficient condition for Hamilton circles in Cayley graphs

Extends Hamilton cycle concepts to infinite, locally finite graphs

Uses topological methods in graph theory

Abstract

For locally finite infinite graphs the notion of Hamilton cycles can be extended to Hamilton circles, homeomorphic images of $S^1$ in the Freudenthal compactification. In this paper we prove of a sufficient condition for the existence of Hamilton circles in locally finite Cayley graphs.