Order

, Volume 14, Issue 1, pp 9–20 | Cite as

Set-Homogeneous Graphs and Embeddings of Total Orders

  • Manfred Droste
  • Michele Giraudet
  • Dugald Macpherson
Article

Abstract

We construct uncountable graphs in which any two isomorphic subgraphs of size at most 3 can be carried one to the other by an automorphism of the graph, but in which some isomorphism between 2-element subsets does not extend to an automorphism. The corresponding phenomenon does not occur in the countable case. The construction uses a suitable construction of infinite homogeneous coloured chains.

k-homogeneous graphs homogeneous chains linear orderings 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Droste, M. (1986) Complete embeddings of linear orderings and embeddings of lattice ordered groups, Israel J. Math. 56, 315–334.Google Scholar
  2. 2.
    Droste, M. and Macpherson, H. D. (1991) On k-homogeneous posets and graphs, J. Comb. Theory Ser. A 56, 1–15.Google Scholar
  3. 3.
    Droste, M. and Shelah, S. (1985) A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets, Israel J. Math. 51, 223–261.Google Scholar
  4. 4.
    Droste, M., Giraudet, M. and Macpherson, H. D. (1995) Periodic ordered permutation groups and cyclic orderings, J. Comb. Theory Ser. B 63, 310–321.Google Scholar
  5. 5.
    Droste, M., Giraudet, M., Macpherson, H. D. and Sauer, N. (1994) Set-homogeneous graphs, J. Comb. Theory Ser. B 62, 63–95.Google Scholar
  6. 6.
    Fraïsse, R. (1986) Theory of Relations, North-Holland, Amsterdam.Google Scholar
  7. 7.
    Mekler, A. H. (1993) Homogeneous partially ordered sets, in N. W. Sauer, R. E. Woodrow and B. Sands (eds), Finite and Infinite Combinatorics in Sets and Logic, Proceedings NATO ASI conference in Banff 1991, Kluwer, Dordrecht, pp. 279–288Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Manfred Droste
    • 1
  • Michele Giraudet
    • 2
  • Dugald Macpherson
    • 3
  1. 1.Institut für Algebra, Technische Universität DresdenDresdenGermany
  2. 2.ParisFrance
  3. 3.Department of Pure MathematicsUniversity of LeedsLeedsEngland

Personalised recommendations