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arXiv · 1403.1472

Long paths in random Apollonian networks

Colin Cooper·Alan Frieze
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Abstract

We consider the length $L(n)$ of the longest path in a randomly generated Apollonian Network (ApN) ${\cal A}_n$. We show that w.h.p. $L(n)\leq ne^{-\log^cn}$ for any constant $c<2/3$.

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Colin Cooper, Alan Frieze. 2014-02-07. Long paths in random Apollonian networks. https://arxiv.org/abs/1403.1472

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