Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws

TL;DR

This paper extends Hamiltonicity conditions from finite to locally finite graphs using topological circles, focusing on claw-free and paw-free forbidden induced subgraphs, advancing understanding of infinite graph cycles.

Contribution

It generalizes a finite graph Hamiltonicity criterion to locally finite graphs employing topological cycles and forbidden subgraph conditions.

Findings

Established Hamiltonicity criteria for locally finite graphs

Utilized topological circles in the Freudenthal compactification

Extended finite graph results to infinite graph contexts

Abstract

In this paper we extend a result about a sufficient condition for Hamiltonicity for finite graphs by Broersma and Veldmann to locally finite graphs. In order to do this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. The condition we focus on in this paper is in terms of forbidden induced subgraphs, namely being claw-free and a relaxation of being paw-free.