As a consequence, these calibrations provide a substantial extension of the previous empirical works devoted to giant stars both in temperature and metallicity ranges. Furthermore, the following points must be stressed after the analysis of the results:
(I) The comparison of the present temperature scale of giants with that of main sequence stars obtained previously with the same procedure (Paper III) shows that in general, gravity is a non negligible parameter in the calibration of temperatures against colours. Indeed, its effect is considerable for (B-V), (V-R), (V-I), (J-K) and (J-H); however, (R-I) and (V-K) have revealed themselves as temperature indicators with negligible dependence on gravity.
(II) For giant stars, in the range of temperatures studied, (V-I), (I-K), (J-K) and to a lesser extent (V-K) are temperature indicators free of blanketing effects (i.e. non-dependent on metallicity). For this reason, their use is preferable as temperature indicators for stars of unknown metallicity. However, the effect of metallicity cannot be neglected for (U-V), (B-V), (V-R), (R-I), (J-H), (u-b) and (b-y).
(III) Concerning the comparison of the present calibrations with previous works, we have to make the following distinction. On the one hand, theoretical calibrations are in general very different both from each other and from empirical relations derived in this work. The trend and the size of the observed discrepancies seem too large to be ascribed only to accidental errors on photometry and uncertainties affecting the effective temperature determinations. Therefore they suggest the persistence of essential problems in the theory of stellar atmospheres (e.g. opacities in bands U and B, convection treatment) and/or the synthesis of colours (e.g. difficulties on the adequate reconstruction of Johnson UBV system). On the other hand, the level of agreement found between (semi-)empirical calibrations based on independent approaches and the present work is fairly good, although there remain uncertainties in the zero point of the scale, and systematic differences under 4000 K and over 5500 K.
In summary, this work demonstrates the necessity of considering the
effect of metallicity and gravity on the relations which
link effective temperatures with intrinsic colours and bolometric
corrections of giants stars.
Therefore, we must conclude by emphasizing that
differences found between the present empirical calibration and other (semi)-empirical and theoretical ones might have relevant consequences on population synthesis and on the transformation of isochrones from the theoretical HR diagram into observed colour-magnitude diagrams.
The most obvious effect regarding the latter, being the variation of the shape and location of the red
giant branch, which has in turn influence on the
interpretation of the ages (when derived from the subgiant branch
colour extension), reddenings and metal content of globular clusters, and even on
the choice of the free parameter 
in the theory of convection
(i.e. the ratio of the mixing length to the pressure scale height). Furthermore, the implications of the
observed discrepancies should also be taken into account when applying calibrations to the determination
of temperatures of individual stars from photometric colours, and to
the analysis of colours synthesized from model atmospheres.
Acknowledgements
We thank Dr. Carlos Allende and Dr. Maurizio Salaris for many helpful discussions on different points of this work. We are grateful to the referee, Dr. Lynas-Gray, for many helpful comments and suggestions which have certainly improved the final version of this paper. We have made use in this research of the SIMBAD database, operated at CDS, Strasbourg, France.
Copyright The European Southern Observatory (ESO)