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Approximating Cayley Diagrams Versus Cayley Graphs

Published online by Cambridge University Press:  04 January 2012

ÁDÁM TIMÁR
ÁDÁM TIMÁR*
Affiliation:
Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090 Wien, Austria (e-mail: madaramit@gmail.com)
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Abstract

We construct a sequence of finite 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 Hamiltonian cycle in one of them has a limit that is not approximable by any subgraph of the other. We give an example where this holds, but convergence is meant in a stronger sense. This is related to whether having a Hamiltonian cycle is a testable graph property.

Keywords

Primary 68R1020F65

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 4 , July 2012 , pp. 635 - 641
Copyright
Copyright © Cambridge University Press 2012

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