  In the context of the gauge/gravity duality, using the proposed candidate
$c$-function, which is derived from the entanglement entropy of a strip-shaped
region, we investigate the RG flow for $d+1$-dimensional quantum field theories
with broken Lorentz and rotational symmetries in the IR, but preserved
conformal invariance in the UV boundary. We examine conditions of monotonicity
of the $c$-function for holographic anisotropic theories dual to the Einstein
gravity via the constraints imposed by the null energy conditions. We consider
near UV and IR behaviors and identify the sufficient conditions that guarantee
the $c$ function decreases monotonically along the RG flows.
