We analytically solve the critical dynamics of the Kob-Andersen kinetically constrained model of supercooled liquids on the Bethe lattice, employing a combinatorial argument based on the cavity method. For arbitrary values of graph connectivity $z$ and facilitation parameter $m$, we demonstrate that the critical behavior of the order parameter is governed by equations of motion equivalent to those found in mode-coupling theory. The resulting predictions for the dynamical exponents are validated through direct comparisons with numerical simulations that include both continuous and discontinuous transition scenarios.

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• Glass transition
• Equilibrium lattice models
• Glasses
• Cavity methods
• Kinetically constrained models