We investigate how a phase transition from neutron-star (NS) matter to spin-polarized neutron matter (SPM) affects the equation of state (EOS) and mass-radius relation of NS. While general extension schemes for the EOS allow for high energy densities and pressures inside NSs, we find that a phase transition to SPM excludes extreme regimes in these extensions. Hence, such a phase transition limits the maximum mass of NSs to lie below 2.6−2.9 M , depending on the microscopic nuclear forces used, while significantly larger masses of 3−4 M could be reached without these constraints. Remarkably, this lower maximum mass is in good agreement with recent constraints extracted from the NS merger GW170817 and its electromagnetic counterpart. Assuming the description in terms of SPM to be valid up to densities in the core of NSs, we find that stars with a large spin-polarized domain in their core are ruled out by the gravitational-wave observation GW170817.Motivation.-Neutron star (NS) observations, such as the recent detection of two merging NSs in the gravitational-wave (GW), gamma-ray, and electromagnetic (EM) spectra [1-4], designated as GW170817, GRB 170817A, and AT 2017gfo, respectively, provide crucial constraints on the equation of state (EOS) of dense strongly interacting matter. The EOS is a key quantity for astrophysics and sensitively depends on strong interactions. Hence, it connects astrophysical observations to laboratory experiments at rare isotope beam facilities for the most neutron-rich extremes at RIBF, Japan, and the future FRIB and FAIR facilities in the US and Germany, respectively. While there is a wealth of theoretical models for the EOS of NS matter (see for reviews), obtained from different theories for strong interactions and with various methods, for densities beyond nuclear saturation density n sat ≈ 0.16 fm −3 these models can only be confronted with a limited set of experimental data, e.g., from heavy-ion collisions [8].Neutron stars are the densest objects in the Universe and probe the EOS up to several times saturation density. Neutron-star observations are therefore an ideal source of additional information that complements experimental data and provides powerful constraints for the EOS at higher densities [14,15]. The structure of a NS is described by the mass-radius (M -R) relation, which is an important observational quantity and in a one-to-one correspondence with the EOS: The M -R relation follows from the EOS by solving the Tolman-Oppenheimer-Volkoff (TOV) equations [16,17]. Measuring the M -R relation, and therefore the EOS, observationally is however extremely difficult. On the one hand, NS masses can be determined very precisely for some NSs in binaries [18]. For example, the precise measurement of two two-solar-mass NSs [19-21] established a robust and