On the largest component of subcritical random hyperbolic graphs

We consider the random hyperbolic graph model introduced by [KPK + 10] and then formalized by [GPP12]. We show that, in the subcritical case $α$ > 1, the size of the largest component is n^{1/(2$α$)+o(1)} , thus strengthening a result of [BFM15] which gave only an upper bound of n^{1/$α$+o(1)}.

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