Set-Homogeneous Graphs and Embeddings of Total Orders
BibTeX
@MISC{Droste_set-homogeneousgraphs,
author = {Manfred Droste and Michele Giraudet and Dugald Macpherson},
title = {Set-Homogeneous Graphs and Embeddings of Total Orders},
year = {}
}
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Abstract
This paper is in part a sequel to [5] and [4]. We construct a certain uncountable graph, thereby answering a question on automorphism groups of infinite graphs which was raised in [5]. The method of construction is order-theoretic, and uses ideas from [4]. We first build a certain uncountable totally ordered set, then obtain from it a cyclic ordering, and finally impose a graph structure on this cyclic ordering. Recall from [5] (or initially Fra isse [6]) that a relational structure M is k- set-homogeneous (k a positive integer) if, whenever U and V are isomorphic substructures of M of size k, there is an automorphism of M taking U to V . We say that M is k-set-homogeneous if it is l-set-homogeneous for all l k. Also,
Citations
| 3 | Periodic ordered permutation groups and cyclic orderings - Droste, Giraudet, et al. - 1995 |
| 3 | Fraïssé: Theory of Relations - unknown authors - 1986 |
| 2 | Set-homogeneous graphs - Droste, Giraudet, et al. - 1994 |
| 1 | Complete embeddings of linear orderings and embeddings of lattice ordered groups - Droste - 1986 |
| 1 | On k-homogeneous posets and graphs - Droste, Macpherson - 1991 |
| 1 | A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets - Droste, Shelah - 1985 |
| 1 | Homogeneous partially ordered sets', in Finite and infinite - Mekler - 1991 |
