Hertzsprung-Russell diagram of the full sample of red giants. The density map corresponds to the whole sample (17 377 stars). The grey dots are stars for which a rotational modulation is detected but that are discarded as probable pollution (151 stars). The magenta stars show the positions of the 19 stars removed according to the T_crit criterion. The blue dots represent stars for which a reliable rotation period has been derived (361 stars). See Sect. 3 for details.