Functional Analysis and Its Applications

, Volume 49, Issue 3, pp 189–200 | Cite as

Henson graphs and Urysohn—Henson graphs as Cayley graphs



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.


Cayley graph Henson graph homogeneity random graph regular action Urysohn space 


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  1. [1]
    P. Cameron, “Homogeneous Cayley objects,” European J. Combin., 21:6 (2000), 745–760.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    P. Cameron and K. Johnson, “An investigation on countable B-groups,” Math. Proc. Cambridge Philos. Soc., 102:2 (1987), 223–232.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    P. Cameron and A. Vershik, “Some isometry groups of the Urysohn space,” Ann. Pure Appl. Logic, 143:1–3 (2006), 70–78.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    G. L. Cherlin, “The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments,” Mem. Amer. Math. Soc., 131 (1998), no. 621.Google Scholar
  5. [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. [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.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    C. Even-Zahar and N. Linial, “Triply existentially complete triangle-free graphs,” J. Graph Theory, 78:4 (2015), 305–317.MathSciNetCrossRefGoogle Scholar
  8. [8]
    R. Fra¨issé, “Sur certains relations qui généralisent l’ordre des nombres rationnels,” C. R. Acad. Sci. Paris, 237 (1953), 540–542.MathSciNetGoogle Scholar
  9. [9]
    C. W. Henson, “A family of countable homogeneous graphs,” Pacific J. Math., 38 (1971), 69–83.MathSciNetCrossRefGoogle Scholar
  10. [10]
    P. S. Urysohn, “Sur un espace métrique universel,” C. R. Acad. Sci. Paris, 180 (1925), 803–806.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics Rutgers UniversityNew YorkUSA

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