Courant–Friedrichs–Lewy condition in FDTD is used to define minimal time step to remain stability of the solution. The definition of Courant–Friedrichs–Lewy condition in N-dimensional space says, that
$$ dt(\sum^n_{i=1}\frac{u_{x_i}}{\Delta x_i}) \leq C $$ or $$ dt \leq \frac{C}{\sum^n_{i=1}\frac{u_{x_i}}{\Delta x_i}} $$ where $C$ is a constant and $u_{x_i}$ is a magnitude of velocity.
assume $C=1$ and $u_{x_i}=c$ for any $i$, then for 3D solution we have
$$ dt\leq \frac{1}{c\cdot\sqrt{\left(\frac{1}{\Delta x}\right)^2+\left(\frac{1}{\Delta y}\right)^2+\left(\frac{1}{\Delta z}\right)^2}} $$
the same solution I've seen in "Numerical Electromagnetics. The FDTD Method" by Inan U.S., Marshall R.A. in chapter 5.3
but in original Yee article there is $$ c\Delta t < \sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2} $$ or $$ \Delta t < \frac{\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}}{c} $$ equation used. And I cannot get the reason of that because for, f.e., $\Delta x = 1$ difference between these two equations is about 10 times, but solution still remains stable for $\Delta t=0.4*\Delta t_2$ and results seem to be the same for the same time interval for the both time steps