The thermal conductivity of monolayer graphene is widely believed to surpass that of diamond even for few-micron-size samples and was proposed to diverge with system size. Here, we predict the thermal conductivity from first principles by considering four-phonon scattering, phonon renormalization, an exact solution to the phonon Boltzmann transport equation (BTE), and a dense enough sampling grid. We show that at room temperature, the thermal conductivity saturates at 10 $\mu \mathrm{m}$ system size and converges to 1300 W/($\mathrm{m}\mathrm{K}$), which is lower than that of diamond. This indicates that four-phonon scattering overall contributes 57% to the total thermal resistance and becomes the leading phonon scattering mechanism over three-phonon scattering. On the contrary, considering three-phonon scattering only yields higher-than-diamond values and divergence with size due to the momentum-conserving normal processes of flexural phonons.

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• Phonons
• Thermal conductivity
• Graphene
• First-principles calculations