  We discuss the BCS theory for electrons in graphene with a superimposed
electrical unidirectional superlattice potential (SL). New Dirac points emerge
together with van Hove singularities (VHS) linking them. We obtain a
superconducting transition temperature $ T_c $ for chemical potentials close to
the VHS assuming that acoustic phonon coupling should be the dominant
mechanism. Pairing of two onsite electrons with one electron close to the $
{\bf K} $ and the other close to the $ -{\bf K} $ point is the most stable pair
formation. The resulting order parameter is almost constant over the entire SL.
