  We propose a mechanism for robust BCS-like superconductivity in graphene
placed in the vicinity of a Bose-Einstein condensate. Electrons in the graphene
interact with the excitations above the condensate, called Bogoliubov
quasiparticles (or bogolons). It turns out that bogolon-pair-mediated
interaction allows us to surpass the long-standing problem of the vanishing
density of states of particles with a linear spectrum. This results in a
dramatic enhancement of the superconducting properties of graphene while
keeping its relativistic dispersion. We study the behavior of the
superconducting gap and calculate critical temperatures in cases with
single-bogolon and bogolon-pair-mediated pairing processes, accounting for the
complex band structure of graphene. We also compare the critical temperature of
the superconducting transition with the BKT temperature.
