Discovering new materials with ultrahigh thermal conductivity has been a critical research frontier and driven by many important technological applications ranging from thermal management to energy science. Here we have rigorously investigated the fundamental lattice vibrational spectra in ternary compounds and determined the thermal conductivity using a predictive ab initio approach. Phonon transport in $\mathrm{B}-X-\mathrm{C}$ $(X=\mathrm{N},\mathrm{P},\mathrm{As})$ groups is systematically quantified with different crystal structures and high-order anharmonicity involving a four-phonon process. Our calculation found an ultrahigh room-temperature thermal conductivity through strong carbon-carbon bonding up to $2100{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ beyond most common materials and the recently discovered boron arsenide. This study provides fundamental insight into the atomistic design of thermal conductivity and opens up opportunities in new materials searching towards complicated compound structures.

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• Phonons
• Thermal conductivity
• Density functional calculations