Approximating Cayley diagrams versus Cayley graphs

Details Approximating Cayley diagrams versus Cayley graphs Approximating Cayley diagrams versus Cayley graphs

2011-03-25

arxiv.org/abs/1103.4968v3

Mathematics

Combinatorics

8 pages, 1 figure

Scientific paper

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 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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