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Approximating Cayley graphs versus Cayley diagrams

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Publikationsdatum 2012
Autor/in Adam Timar,
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Combinatorics, probability and computing
Volume (Issue) 21
Seite(n) 635 - 641
Titel der Proceedings Combinatorics, probability and computing

Open Access

URL http://arxiv.org/pdf/1103.4968.pdf
OA-Form Repositorium (Green Open Access)

Abstract

We construct a sequence of nite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that converge to the same limit, and such that a spanning tree in one of them has a limit that is not approximable by any subgraph of the other. We give an example where this subtree is a Hamiltonian cycle, but convergence is meant in a stronger sense. These latter are related to whether having a Hamiltonian cycle is a testable graph property.
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