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arXiv · 1203.5069

Random Regular Graphs are not Asymptotically Gromov Hyperbolic

Gabriel H. Tucci
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Abstract

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 $δ$--hyperbolic for any non--negative $δ$ almost surely as $n\to\infty$.

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Gabriel H. Tucci. 2012-03-22. Random Regular Graphs are not Asymptotically Gromov Hyperbolic. https://arxiv.org/abs/1203.5069

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