  We study the question of the gauge dependence of the quantum gravity
contribution to the running gauge coupling constant for electromagnetism. The
calculations are performed using dimensional regularization in a manifestly
gauge invariant and gauge condition independent formulation of the effective
action. It is shown that there is no quantum gravity contribution to the
running charge, and hence there is no alteration to asymptotic freedom at high
energies as predicted by Robinson and Wilczek.
