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Homogeneous graphs and stability
Published online by Cambridge University Press: 09 April 2009
Abstract
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Let Γ be a graph with finite vertex set V. Γ is homogeneous if whenever U1, U2 ⊆ V are such that the vertex subgraphs (U1), (U2) are isomorphic, then every isomorphism from (U1) to (U2) extends to an automorphism of Γ; homogeneous graphs were studied by Sheehan (1974) and were classified by the author. Γ is locally homogeneous if whenever U ⊆ V, then every automorphism of (U) extends to an automorphism of Γ. We prove that every locally homogeneous graph is homogeneous.
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- Copyright © Australian Mathematical Society 1976
References
Gardiner, A. (to appear), ‘Homogeneous graphs’, J. Combinatorial Theory.Google Scholar
Sheehan, J. (1974), ‘Smoothly embeddable subgraphs’, J. London Math. Soc. (2), 9, 212–218.CrossRefGoogle Scholar
Yap, H. P. (1974), ‘Some remarks on stable graphs’, Bull. Austral. Math. Soc. 10, 351–357.CrossRefGoogle Scholar
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