  In the present paper we investigate the structure of relativistic stars in 4D
Einstein-Gauss-Bonnet gravity. The mass-radius relations are obtained for
realistic hadronic and for strange quark star equations of state, and for a
wide range of the Gauss-Bonnet coupling parameter $\alpha$. Even though the
deviations from general relativity for nonzero values of $\alpha$ can be large
enough, they are still comparable with the variations due to different modern
realistic equations of state if we restrict ourselves to moderate value of
$\alpha$. That is why the current observations of the neutron star masses and
radii alone can not impose stringent constraints on the value of the parameter
$\alpha$. Nevertheless some rough constraints on $\alpha$ can be put. The
existence of stable stellar mass black holes imposes $\sqrt{\alpha}\lesssim 2.6
{\rm km}$ for $\alpha>0$ while the requirement that the maximum neutron star
mass should be greater than two solar masses gives $\sqrt{|\alpha|}\lesssim 3.9
{\rm km}$ for $\alpha<0$. We also present an exact solution describing the
structure of relativistic stars with uniform energy density in 4D
Einstein-Gauss-Bonnet gravity.
