TL;DR
This paper surveys the unique countably infinite random graph discovered by Erdős and Rényi, focusing on its properties and automorphism group, highlighting its significance in graph theory and symmetry studies.
Contribution
It provides a comprehensive overview of the properties and automorphism group of the unique countably infinite random graph, consolidating existing knowledge.
Findings
The graph is highly symmetric and unique among infinite graphs.
Its automorphism group exhibits rich symmetry properties.
The survey clarifies the role of this graph in mathematical theory.
Abstract
Erd\H{o}s and R\'{e}nyi showed the paradoxical result that there is a unique (and highly symmetric) countably infinite random graph. This graph, and its automorphism group, form the subject of the present survey.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory