  Polyatomic polar molecules are promising systems for future experiments that
search for violation of time-reversal and parity symmetries due to their
advantageous electronic and vibrational structure, which allows laser cooling,
full polarisation of the molecule, and reduction of systematic effects [I.
Kozyryev and N.R. Hutzler, Phys, Rev. Lett. {\bf 119}, 133002 (2017)]. In this
work we investigate the enhancement factor of the electric dipole moment of the
electron ($E_\text{eff}$) in the triatomic monohydroxide molecules BaOH and
YbOH within the high-accuracy relativistic coupled cluster method. The
recommended $E_\text{eff}$ values of the two systems are 6.65 $\pm$ 0.15 GV/cm
and 23.4 $\pm$ 1.0 GV/cm, respectively. We compare our results with similar
calculations for the isoelectronic diatomic molecules BaF and YbF, which are
currently used in experimental search for $P,T$-odd effects in molecules. The
$E_\text{eff}$ values prove to be very close, within about 1.5 $\%$ difference
in magnitude between the diatomic and the triatomic compounds. Thus, BaOH and
YbOH have a similar enhancement of the electron electric dipole moment, while
benefiting from experimental advantages, and can serve as excellent candidates
for next-generation experiments.
