  Recent X-ray variability observations of accreting neutron stars may provide
the first evidence for frame dragging effects around spinning relativistic
objects. Motivated by this possibility and its implications for neutron-star
structural properties, we calculate new optimal bounds on the masses, radii,
and moments of inertia of slowly rotating neutron stars that show kilohertz
quasi-periodic oscillations (QPOs). These bounds are derived under minimal
assumptions about the properties of matter at high densities and therefore are
largely independent of the unknown equation of state. We further derive a
semi-analytical upper bound on the neutron-star moment of inertia without
making any assumptions about the equation of state of matter at any density. We
use this upper bound to show that the maximum possible nodal precession
frequency of an inclined circular orbit around a slowly spinning neutron star
is nu_{NP}~45.2 (nu_s/300Hz) Hz, where nu_s is the spin frequency of the
neutron star. We conclude that the nodal-precession interpretation of
low-frequency QPOs in accreting neutron stars is inconsistent with their
inferred spin frequencies or the identification of the highest-frequency QPO
with that of a circular Keplerian orbit in the accretion disk.
