  Statistical analysis of the eigenfunctions of the Anderson tight-binding
model with on-site disorder on regular random graphs strongly suggests that the
extended states are multifractal at any finite disorder. The spectrum of
fractal dimensions $f(\alpha)$ defined in Eq.(3), remains positive for $\alpha$
noticeably far from 1 even when the disorder is several times weaker than the
one which leads to the Anderson localization, i.e. the ergodicity can be
reached only in the absence of disorder. The one-particle multifractality on
the Bethe lattice signals on a possible inapplicability of the equipartition
law to a generic many-body quantum system as long as it remains isolated.
