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dc.contributor.authorJonusas, Julius
dc.contributor.authorMitchell, J. D.
dc.identifier.citationJonusas , J & Mitchell , J D 2017 , ' Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs ' , Forum Mathematicum , vol. 29 , no. 4 , pp. 905-939 .
dc.identifier.otherPURE: 241708365
dc.identifier.otherPURE UUID: b703ca57-e32a-4853-9e52-e91068a27778
dc.identifier.otherScopus: 85023200346
dc.identifier.otherWOS: 000405334600009
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700827
dc.description.abstractA countable graph is ultrahomogeneous if every isomorphism between finite induced subgraphs can be extended to an automorphism. Woodrow and Lachlan showed that there are essentially four types of such countably infinite graphs: The random graph, infinite disjoint unions of complete graphs Kn with n ò Nvertices, the Kn-free graphs, finite unions of the infinite complete graph K, and duals of such graphs. The groups Aut(λ) of automorphisms of such graphs λ have a natural topology, which is compatible with multiplication and inversion, i.e. The groupsAut(λ) are topological groups.We consider the problem of finding minimally generated dense subgroups of the groups Aut(λ) where λ is ultrahomogeneous.We show that if λ is ultrahomogeneous, then Aut(λ) has 2-generated dense subgroups, and that under certain conditions given f ò Aut(λ) there exists g ò Aut(λ) such that the subgroup generated by f and g is dense. We also show that, roughly speaking, g can be chosen with a high degree of freedom. For example, if λ is either an infinite disjoint union of Kn or a finite union of Kω, then g can be chosen to have any given finite set of orbit representatives.
dc.relation.ispartofForum Mathematicumen
dc.rights© 2017 Walter de Gruyter GmbH, Berlin/Boston.. This work has been made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at
dc.subjectAutomorphism groupsen
dc.subjectFraïssé limitsen
dc.subjectPolish groupsen
dc.subjecttopological generationen
dc.subjectQA Mathematicsen
dc.titleTopological 2-generation of automorphism groups of countable ultrahomogeneous graphsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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