Non-perturbative QEG corrections to the Yang-Mills beta function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. Our result is consistent with the conjecture that quantum Einstein gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.