  We discuss the possibility of superconductivity in graphene taking into
account both electron-phonon and electron-electron Coulomb interactions. The
analysis is carried out assuming that the Fermi energy is far away from the
Dirac points, such that the density of the particles (electrons or holes) is
high. We derive proper Eliashberg equations that allow us to estimate the
critical superconducting temperature. The most favorable is pairing of
electrons belonging to different valleys in the spectrum. Using values of
electron-phonon coupling estimated in other publications we obtain the critical
temperature T_c as a function of the electron (hole) density. This temperature
can reach the order of 10 K at the Fermi energy of order 1-2 eV. We show that
the dependence of the intervalley pairing on the impurity concentration should
be weak.
