We study relaxation of an excited electron in the conduction band of intrinsic graphene at zero temperature due to production of interband electron-hole pairs by Coulomb interaction. The electronic band curvature, being anisotropic because of trigonal warping, is shown to suppress relaxation for a range of directions of the initial electron momentum. For other directions, relaxation is allowed only if the curvature exceeds a finite critical value; otherwise, a non-decaying quasiparticle state is shown to exist.