  By analyzing an $e^+e^-$ annihilation data sample with an integrated
luminosity of $2.93\ \rm fb^{-1}$ taken at the center-of-mass energy of 3.773
GeV with the BESIII detector, we determine the absolute branching fractions of
the hadronic decays $D^0\to K^-\pi^+\omega$, $D^0\to K^0_S\pi^0\omega$, and
$D^+\to K^0_S\pi^+\omega$ to be $(3.392 \pm 0.044_{\rm stat} \pm 0.085_{\rm
syst})\%$, $(0.848 \pm 0.046_{\rm stat} \pm 0.031_{\rm syst})\%$, and $(0.707
\pm 0.041_{\rm stat} \pm 0.029_{\rm syst})\%$, respectively. The accuracy of
the branching fraction measurement of the decay $D^0\to K^-\pi^+\omega$ is
improved by a factor of seven compared to the world average value. The
$D^{0}\to K^0_S\pi^{0}\omega$ and $D^{+}\to K^0_S\pi^{+}\omega$ decays are
observed for the first time.
