  The effect of Coulomb interaction in an ensemble of Dirac fermions on the
formation of superconducting pairing in monolayer and bilayer doped graphene is
studied using the Kohn-Luttinger mechanism disregarding the Van der Waals
potential of the substrate and impurities. The electronic structure of graphene
is described using the Shubin-Vonsovsky model taking into account the
intratomic, interatomic, and interlayer (in the case of bilayer graphene)
Coulomb interactions between electrons. The Cooper instability is determined by
solving the Bethe-Saltpeter integral equation. The renormalized scattering
amplitude is obtained with allowance for the Kohn-Luttinger polarization
contributions up to the second order of perturbation theory in the Coulomb
interaction. It plays the role of effective interaction in the Bethe-Salpeter
integral equation. It is shown that the allowance for the Kohn-Luttinger
renormalizations as well as intersite Coulomb interaction noticeably affects
the competition between the superconducting phases with the $f-$wave and $d +
id-$wave symmetries of the order parameter. It is demonstrated that the
superconducting transition temperature for an idealized graphene bilayer with
significant interlayer Coulomb interaction between electrons is noticeably
higher than in the monolayer case.
