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Henson graphs and Urysohn—Henson graphs as Cayley graphs

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Abstract

We discuss groups acting regularly on the Henson graphs Γ n , answering a question posed by Peter Cameron, and we explore a number of related questions.

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References

  1. P. Cameron, “Homogeneous Cayley objects,” European J. Combin., 21:6 (2000), 745–760.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Cameron and K. Johnson, “An investigation on countable B-groups,” Math. Proc. Cambridge Philos. Soc., 102:2 (1987), 223–232.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Cameron and A. Vershik, “Some isometry groups of the Urysohn space,” Ann. Pure Appl. Logic, 143:1–3 (2006), 70–78.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. L. Cherlin, “The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments,” Mem. Amer. Math. Soc., 131 (1998), no. 621.

  5. G. Cherlin, “Two problems on homogeneous structures, revisited,” in: Model Theoretic Methods in Finite Combinatorics, Contemporary Math., vol. 558, Amer. Math. Soc., Providence, RI, 2011, 319–415.

    Google Scholar 

  6. M. El-Zahar and N. Sauer, “The indivisibility of the homogeneous Kn-free graphs,” J. Combin. Theory Ser. B, 47:2 (1989), 162–170.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. Even-Zahar and N. Linial, “Triply existentially complete triangle-free graphs,” J. Graph Theory, 78:4 (2015), 305–317.

    Article  MathSciNet  Google Scholar 

  8. R. Fra¨issé, “Sur certains relations qui généralisent l’ordre des nombres rationnels,” C. R. Acad. Sci. Paris, 237 (1953), 540–542.

    MathSciNet  Google Scholar 

  9. C. W. Henson, “A family of countable homogeneous graphs,” Pacific J. Math., 38 (1971), 69–83.

    Article  MathSciNet  Google Scholar 

  10. P. S. Urysohn, “Sur un espace métrique universel,” C. R. Acad. Sci. Paris, 180 (1925), 803–806.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Rutgers University, New York, USA

    Gregory Cherlin

Authors
  1. Gregory Cherlin
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Correspondence to Gregory Cherlin.

Additional information

Dedicated to Professor Anatoly Vershik on the occasion of his 80th birthday

Supported by the Hausdorff Institute for Mathematics, Bonn, Fall 2013 Trimester, and NSF DMS-1101597. A draft of this article was originally published as an HIM preprint.

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 3, pp. 41–56, 2015

Original Russian Text Copyright © by Gregory Cherlin

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Cherlin, G. Henson graphs and Urysohn—Henson graphs as Cayley graphs. Funct Anal Its Appl 49, 189–200 (2015). https://doi.org/10.1007/s10688-015-0103-2

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  • DOI: https://doi.org/10.1007/s10688-015-0103-2

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