We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T-c, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T << T-c, and zero magnetic field, the density of states is characterized by a small gap E-g <= T-c resulting from the collective proximity effect. Transverse magnetic field H-g(T) proportional to E-g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H(g)2(T).
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