Long paths in random Apollonian networks
classification
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apollonianconsiderconstantgeneratedlengthlonglongestnetwork
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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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