  It is likely that at least some planetary nebulae are composed of matter
which was ejected from a binary star system during common-envelope (CE)
evolution. For these planetary nebulae the ionizing component is the hot and
luminous remnant of a giant which had its envelope ejected by a companion in
the process of spiralling-in to its current short-period orbit. A large
fraction of CE phases which end with ejection of the envelope are thought to be
initiated by low-mass red giants, giants with inert, degenerate helium cores.
We discuss the possible end-of-CE structures of such stars and their subsequent
evolution to investigate for which structures planetary nebulae are formed. We
assume that a planetary nebula forms if the remnant reaches an effective
temperature greater than 30 kK within 10^4 yr of ejecting its envelope. We
assume that the composition profile is unchanged during the CE phase so that
possible remnant structures are parametrized by the end-of-CE core mass,
envelope mass and entropy profile. We find that planetary nebulae are expected
in post-CE systems with core masses greater than about 0.3 solar masses if
remnants end the CE phase in thermal equilibrium. We show that whether the
remnant undergoes a pre-white dwarf plateau phase depends on the prescribed
end-of-CE envelope mass. Thus, observing a young post-CE system would constrain
the end-of CE envelope mass and post-CE evolution.
