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Construction of Some Uncountable 2-Arc-Transitive Bipartite Graphs

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Abstract

We give various constructions of uncountable arc-transitive bipartite graphs employing techniques from partial orders, starting with the cycle-free case, but generalizing to cases where this may be violated.

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References

  1. Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society Colloquium Publications. American Mathematical Society, Providence (1967)

  2. Creed, P., Truss, J.K., Warren, R.: The structure of k-CS-transitive cycle-free partial orders with infinite chains. Math. Proc. Camb. Philos. Soc. 126, 175–194 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  4. Droste, M.: Structure of partially ordered sets with transitive automorphism groups. Mem. Am. Math. Soc. 57, 334 (1985)

    MathSciNet  Google Scholar 

  5. Goldstern, M., Grossberg, R., Kojman, M.: Infinite homogeneous bipartite graphs with unequal sides. Discrete Math. 149(1-3), 69–82 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gray, R., Truss, J.K.: Construction of some countable one-arc-transitive bipartite graphs. Discrete Math. (in press)

  7. Gray, R., Truss, J.K.: Cycle-free partial orders and ends of graphs. Math. Proc. Camb. Philos. Soc. (in press)

  8. Hrushovski, E.: Extending partial isomorphisms of graphs. Combinatorica 12, 411–416 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kojman, M., Shelah, S.: Homogeneous families and their automorphism groups. J. Lond. Math. Soc. 52, 303–317 (1995)

    MATH  MathSciNet  Google Scholar 

  10. Giudici, M., Cai, H., Praeger, C.E.: Analysing finite locally s-arc transitive graphs. Trans. Am. Math. Soc. 356, 291–317 (2004)

    Article  MATH  Google Scholar 

  11. Truss, J.K.: Betweenness relations and cycle-free partial orders. Math. Proc. Camb. Philos. Soc. 119, 631–643 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Truss, J.K.: On k-CS-transitive cycle-free partial orders with finite alternating chains. Order 15, 151–165 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Warren, R.: The structure of k-CS-transitive cycle-free partial orders. Mem. Am. Math. Soc. 129, 614 (1997)

    Google Scholar 

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Authors and Affiliations

  1. Universität Leipzig, Leipzig, Germany

    Manfred Droste

  2. University of St Andrews, St Andrews, Scotland

    Robert Gray

  3. University of Leeds, Leeds, UK

    John K. Truss

Authors
  1. Manfred Droste
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  2. Robert Gray
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  3. John K. Truss
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Corresponding author

Correspondence to John K. Truss.

Additional information

This work was supported by a grant from the EPSRC.

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Droste, M., Gray, R. & Truss, J.K. Construction of Some Uncountable 2-Arc-Transitive Bipartite Graphs. Order 25, 349–357 (2008). https://doi.org/10.1007/s11083-008-9098-0

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  • DOI: https://doi.org/10.1007/s11083-008-9098-0

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