  Recently, traversable wormhole geometries were constructed in the context of
f(R) gravity. The latter is equivalent to a Brans-Dicke theory with a coupling
parameter w=0, which is apparently excluded from the narrow interval,
-3/2<w<-4/3, extensively considered in the literature of static wormhole
solutions in vacuum Brans-Dicke theory. However, this latter interval is only
valid for a specific choice of an integration constant of the field equations
derived on the basis of a post-Newtonian weak field approximation, and there is
no reason for it to hold in the presence of compact objects with strong
gravitational fields. In this context, we construct a general class of vacuum
Brans-Dicke wormholes that include the value of w=0. Furthermore, we present
the general condition for the existence of vacuum Brans-Dicke wormhole
geometries, and show that the presence of effective negative energy densities
is a generic feature of these vacuum solutions.
