Abstract
In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finite infinite graphs. For this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. In this paper we focus on conditions involving claws, nets and bulls as induced subgraphs. We extend Hamiltonicity results for finite claw-free and net-free graphs by Shepherd to locally finite graphs. Moreover, we generalise a classification of finite claw-free and net-free graphs by Shepherd to locally finite ones. Finally, we extend to locally finite graphs a Hamiltonicity result by Ryjáček involving a relaxed condition of being bull-free.
| Original language | English |
|---|---|
| Pages (from-to) | 23-47 |
| Number of pages | 25 |
| Journal | Journal of Graph Theory |
| Volume | 103 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - May 2023 |
Bibliographical note
Funding Information:Karl Heuer was supported by a postdoc fellowship of the German Academic Exchange Service (DAAD) and by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC consolidator grant DISTRUCT, Agreement No. 648527). Deniz Sarikaya is thankful for the financial and ideal support of the Studienstiftung des deutschen Volkes and of the Claussen‐Simon‐Stiftung. Furthermore, both authors would like to thank Max Pitz for a comprehensive feedback on an early draft of this paper. Also they would like to thank Hendrik Niehaus and J. Pascal Gollin for helpful comments on an early version of this article.
Publisher Copyright:
© 2022 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
Keywords
- ends of infinite graphs
- forbidden induced subgraphs
- Freudenthal compactification
- Hamiltonicity
- locally finite graphs