The onset of variability in red giant stars is studied from the data c
ollected by the 'Long-Term Photometry of Variables' project which oper
ates at ESO (La Silla) since 1982. The differential nature of the obse
rvations combined with a multi-night reduction algorithm enables to st
udy the variability of over 50 red giants with an accuracy of the orde
r of 2 to 3 millimagnitudes on time scales ranging from days to years.
All red giants with spectral types late G to early K (i.e. b - y simi
lar to 0.6 - 0.8) are stable at the level sigma(y) < 6 millimag (where
sigma(y) is the standard deviation of the Stromgren y magnitude). Red
giants with later spectral types are all variable, and it is found th
at the minimum variability level sigma(y,min) increases with increasin
g b-y, thus defining a minimum-variability boundary. The new data obta
ined in this paper reveal that the time scale of the associated variab
ility increases with increasing b - y (and thus amplitude), and that t
he stability of this time scale improves concomitantly. More precisely
, irregular variations on time scales of 5 to 10 days (and sigma(y) si
milar to 7 millimag) characterize red giants with b-y similar to 1.0)
whereas the variations (with sigma(y) similar to 100 millimag) become
more regular with periods of the order of 50 d for red giants with b -
y similar to 1.3. A radial-velocity jitter (of the order of 1.5 km s(
-1) r.m.s.) is associated with this photometric variability, and sugge
sts that stellar oscillations may be responsible for the observed vari
ations.