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 $\alpha$ > 1, the size of the largest component is n^{1/(2$\alpha$)+o(1)} , thus strengthening a result of [BFM15] which gave only an upper bound of n^{1/$\alpha$+o(1)}.