Finite Transitive Graph Embeddings into a Hyperbolic Metric Space Must Stretch or Squeeze
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The δ-hyperbolicity constant of a finite vertex transitive graph with more than two vertices is proportional to its diameter. This implies that any map from such a graph into a 1-Gromov hyperbolic metric space has to stretch or squeeze the metric.
Keywordsﬁnite Vertex-transitive Graphs Geodesic Triangle Gromov Hyperbolic Groups Quasi Proof Geodesic Segment
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