  The detection of the GW170817 neutron star merger event has incited an
intense research activity towards the understanding of the nuclear matter
equation of state. In this paper we compare in particular the pressure-density
relation obtained from heavy-ion collisions with the analysis of the NS merger
event. Moreover, we present recent calculations of neutron star's moment of
inertia and tidal deformability using various microscopic equations of state
for nuclear and hybrid star configurations, and confirm several universal
relations. We also discuss the recent constraints for the NS radii determined
by GW170817, and find compatible radii between 12 and 13 kilometers, thus
identifying the suitable equations of state.
