A representation theorem for end spaces of infinite graphs
Abstract
Abstract End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can be topologically represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree.
Fields of Study & Subjects
Advanced Graph Theory Research
Limits and Structures in Graph Theory
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 2
- Pages
- 1021–1047
- Publication date
- 16 April 2026
- Language
- EN