Order

, Volume 14, Issue 1, pp 9–20

Set-Homogeneous Graphs and Embeddings of Total Orders

  • Manfred Droste
  • Michele Giraudet
  • Dugald Macpherson
Article

DOI: 10.1023/A:1005880810385

Cite this article as:
Droste, M., Giraudet, M. & Macpherson, D. Order (1997) 14: 9. doi:10.1023/A:1005880810385

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 graphshomogeneous chainslinear orderings

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