(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.