  Starting from the ELSV formula, we derive a number of new equations on the
generating functions for Hodge integrals over the moduli space of complex
curves. This gives a new simple and uniform treatment of certain known results
on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's
lambda_g conjecture etc. Among other results we show that a properly arranged
generating function for Hodge integrals satisfies the equations of the KP
hierarchy.
