  We identify an observable imprint of a first-order hadron-quark phase
transition at supranuclear densities on the gravitational-wave (GW) emission of
neutron star mergers. Specifically, we show that the dominant postmerger GW
frequency f_peak may exhibit a significant deviation from an empirical relation
between f_peak and the tidal deformability if a strong first-order phase
transition leads to the formation of a gravitationally stable extended quark
matter core in the postmerger remnant. A comparison of the GW signatures from a
large, representative sample of microphysical, purely hadronic equations of
state indicates that this imprint is only observed in those systems which
undergo a strong first-order phase transition. Such a shift of the dominant
postmerger GW frequency can be revealed by future GW observations, which would
provide evidence for the existence of a strong first-order phase transition in
the interior of neutron stars.
