Gromov hyperbolicity of periodic planar graphs
✍ Scribed by Cantón, Alicia; Granados, Ana; Pestana, Domingo; Rodríguez, José Manuel
- Book ID
- 121591825
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2013
- Tongue
- English
- Weight
- 250 KB
- Volume
- 30
- Category
- Article
- ISSN
- 1439-7617
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## Abstract In this article, the δ‐hyperbolic concept, originally developed for infinite graphs, is adapted to very large but finite graphs. Such graphs can indeed exhibit properties typical of negatively curved spaces, yet the traditional δ‐hyperbolic concept, which requires existence of an upper
If X is a geodesic metric space and 1 2 3 ∈ X , a geodesic triangle T = { 1 2 3 } is the union of the three geodesics [ 1 2 ], [ 2 3 ] and [ 3 1 ] in X . The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for ever