From cycles to circles in Cayley graphs

TL;DR

This paper extends classical theorems on Hamiltonicity from finite Cayley graphs to their infinite counterparts, introducing the concept of Hamilton circles in the context of locally finite infinite graphs.

Contribution

It generalizes well-known finite Cayley graph Hamiltonicity results to infinite graphs using the concept of Hamilton circles.

Findings

Extension of Hamilton cycle theorems to Hamilton circles in infinite graphs

Introduction of Hamilton circles as homeomorphic images of S^1 in the Freudenthal compactification

Broader understanding of Hamiltonicity in infinite Cayley graphs

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 extend some well-known theorems of the Hamiltonicity of finite Cayley graphs to infinite Cayley graphs.