The exciton Wannier equation for graphene is solved for different background dielectric constants. It is shown that freestanding graphene features strong Coulomb effects with a very large exciton binding energy exceeding $3,$eV. A second-order transi
tion to a weak Coulomb regime is found if the effective background dielectric constant exceeds a critical value. All bound-state solutions vanish for epitaxial graphene on a substrate with large background permittivity, such as SiC.
