We study the stability against infinitesimal radial oscillations of neutron stars generated by a set of equations of state obtained from first-principle calculations in cold and dense QCD and constrained by observational data. We consider mild and large violations of the conformal bound, $c_{s} = 1/sqrt{3}$, in stars that can possibly contain a quark matter core. Some neutron star families in the mass-radius diagram become dynamically unstable due to large oscillation amplitudes near the core.
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