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Set-Homogeneous Graphs and Embeddings of Total Orders |
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| Authors: | Manfred Droste Michele Giraudet Dugald Macpherson |
| Affiliation: | (1) Institut für Algebra, Technische Universität Dresden, 01062 Dresden, Germany;(2) 32 rue de la Reunion, 75020 Paris, France;(3) Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, England |
| 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. |
| Keywords: | k-homogeneous graphs homogeneous chains linear orderings |
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