Some constructions of highly arc-transitive digraphs

Abstract

We construct infinite highly arc-transitive digraphs with finite out-valency and whose sets of descendants are digraphs which have a homomorphism onto a directed (rooted) tree. Some of these constructions are based on [4] and [5], and are shown to have universal reachability relation.

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References

  1. [1]

    Daniela Amato: Descendants in infinite, primitive, highly arc-transitive digraphs, Discrete Mathematics 310 (2010), 2021–2036.

    MathSciNet  MATH  Article  Google Scholar 

  2. [2]

    Peter J. Cameron, Cheryl E. Praeger, and Nicholas C. Wormald: Infinite highly arc-transitive digraphs and universal covering digraphs, Combinatorica 13(4) (1993), 377–396.

    MathSciNet  MATH  Article  Google Scholar 

  3. [3]

    Peter J. Cameron: Oligomorphic Permutation Groups, London Mathematical Society Lecture Notes, Vol. 152 Cambridge University Press, 1990.

  4. [4]

    David M. Evans: An infinite highly arc-transitive digraph, Europ. J. Combin. 18 (1997), 281–286.

    MATH  Article  Google Scholar 

  5. [5]

    David M. Evans: Suborbits in infinite primitive permutation groups, Bull. London Math. Soc. 33 (2001), 583–590.

    MathSciNet  MATH  Article  Google Scholar 

  6. [6]

    Josephine Emms and David M. Evans: Constructing continuum many countable, primitive, unbalanced digraphs; Discrete Mathematics 309 (2009), 4475–4480.

    MathSciNet  MATH  Article  Google Scholar 

  7. [7]

    Aleksander Malnič, Dragan Marušič, Norbert Seifter and Boris Zgrablič: Highly arc-transitive digraphs with no homomorphism onto ℤ, Combinatorica 22(3) (2002), 435–443.

    MathSciNet  MATH  Article  Google Scholar 

  8. [8]

    Rögnvaldur G. Möller: Groups acting on locally finite graphs — a survey of the infinitely ended case, Groups’ 93 Galway/St Andrews, Vol. 2, London Math. Soc. Lecture Notes Series 212, Cambridge University Press, Cambridge 1995, pp. 426–456.

    Google Scholar 

  9. [9]

    Rögnvaldur G. Möller: Descendants in highly arc-transitive digraphs, Discrete Math. 247(1–3) (2002), 147–157.

    MathSciNet  MATH  Article  Google Scholar 

  10. [10]

    Peter M. Neumann: Postcript to review of [3], Bull. London Math. Soc. 24 (1992), 404–407.

    Article  Google Scholar 

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Correspondence to Daniela Amato.

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This work was supported by EPSRC grant EP/D04829/1.

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Amato, D., Truss, J.K. Some constructions of highly arc-transitive digraphs. Combinatorica 31, 257 (2011). https://doi.org/10.1007/s00493-011-2523-9

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Mathematics Subject Classification (2000)

  • 05C20
  • 05C38