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On the Structure of Vertex Transitive Graphs

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2100)

Abstract

This short section contains several facts and open problems regarding vertex transitive graphs, starting with the following theorem from [BS92] which refines an earlier result of Aldous.

Keywords

  • Isoperimetric Inequality
  • Isometric Embedding
  • Doubling Property
  • Quantitative Version
  • Graph Minus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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  2. I. Benjamini, H. Finucane, R. Tessera, On the scaling limit of finite vertex transitive graphs with large diameter. arXiv preprint arXiv:1203.5624 Combinatorica (2014)

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  3. E. Breuillard, B. Green, T. Tao, The structure of approximate groups. Publ. Math. lÍHÉS 116(1), 115–221 (2012)

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  4. I. Benjamini, G. Kozma, A resistance bound via an isoperimetric inequality. Combinatorica 25(6), 645–650 (2005)

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  5. L. Babai, M. Szegedy, Local expansion of symmetrical graphs. Comb. Probab. Comput. 1(1), 1–11 (1992)

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© 2013 Springer International Publishing Switzerland

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Benjamini, I. (2013). On the Structure of Vertex Transitive Graphs. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_2

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