  The first detection of gravitational waves from the binary neutron star
merger event GW170817 has started to provide important new constraints on the
nuclear equation of state at high density. The tidal deformability bound of
GW170817 combined with the observed two solar mass neutron star poses a serious
challenge to theoretical formulations of realistic equations of state. We
analyze a fully comprehensive set of relativistic nuclear mean-field theories
by confronting them with the observational bounds and the measured neutron-skin
thickness. We find that only a few models can withstand these bounds which
predict a stiff overall equation of state but with a soft neutron-proton
symmetry energy. Two possible indications are proposed: Circumstantial evidence
of hadron-quark phase transition inside the star and new parametrizations that
are consistent with ground state properties of finite nuclei and observational
bounds. Based on extensive analysis of these sets, an upper limit on the radius
of a $1.4M_\odot$ neutron star of $R_{1.4}\lesssim 12.9$ km is deduced.
