Mass-radius diagram of the companion objects with M < 0.3 M_⊙ found to some of the analyzed KOIs in groups A and B. The open square shows the location of the possible third body in the KOI-3853 (i.e., KOI-3853 C), with an ad hoc assumed radius of 0.1 R_⊙. The dotted vertical error bar indicates our unknown about its actual size, see Sect. 5. We used the isochrones of 1 Gyr and 5 Gyr (from top to bottom) from Baraffe et al. (1998) for solar metallicity (dotted dark blue line) and [Fe/H] = −0.5 (dashed light blue line). In the case of masses below 0.1 M_⊙, we used the Baraffe et al. (2003) isochrones (dotted-dashed gray lines) of 1, 5, and 10 Gyr (from top to bottom). The arrows in the Group B KOIs indicate that their masses are just upper limits. The dashed regions illustrates the range of masses allowed for the KOI-0972 planet candidates (see Sect. 5). For reference, we have plotted the known planets with provided masses and radius published in the exoplanet encyclopedia (www.exoplanet.eu) as light blue plus signs.