Random Regular Graphs are not Asymptotically Gromov Hyperbolic

Details Random Regular Graphs are not Asymptotically Gromov Hyperbolic Random Regular Graphs are not Asymptotically Gromov Hyperbolic

2012-03-22

arxiv.org/abs/1203.5069v1

Mathematics

Metric Geometry

6 pages, 2 figures

Scientific paper

In this paper we prove that random $d$--regular graphs with $d\geq 3$ have
traffic congestion of the order $O(n\log_{d-1}^{3}(n))$ where $n$ is the number
of nodes and geodesic routing is used. We also show that these graphs are not
asymptotically $\delta$--hyperbolic for any non--negative $\delta$ almost
surely as $n\to\infty$.

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