Reduced proper motion (RPM), colour–magnitude, and (H − K_s,J − H) diagrams for the 12 <K_s< 16 M dwarfs selected by colour-based relations (pink contours). Bulge giant stars from the BRaVA project are shown as black open circles. a) In the RPM diagram, likely giants contaminants lie above the black line which represents the as a function of (J − K_s) colour. b) In the CMD, likely giant stars from SPM4 (blue dots) exhibit brighter magnitudes attributable to the magnitude cut of the survey, while PPMXL provides parallaxes for fainter likely giants (red dots). Crosses depict likely giants identified by colour-cuts from Sharma et al. (2010). c) Likely giants selected by colour-cuts (crosses) follow the trend of the BRaVa giants (open circles) in the (H − K_s,J − H) diagram. Likely giants identified by proper motions are mostly located in the upper part of the M dwarf region (redder J − H colours), and exhibit H − K_s colours redder than ~0.13 mag.