Random Constraint Satisfaction Problems exhibit several phase transitions when their density of constraints is varied. One of these threshold phenomena, known as the clustering or dynamic transition, corresponds to a transition for an information theoretic problem called tree reconstruction. In this article we study this threshold for two CSPs, namely the bicoloring of k-uniform hypergraphs with a density α of constraints, and the q-coloring of random graphs with average degree c. We show that in the large k, q limit the clustering transition occurs for, where γ d is the same constant for both models. We characterize γ d via a functional equation, solve the latter numerically to estimate γ d ≈ 0.871, and obtain an analytic lowerbound γ d ≥ 1 + ln(2( √ 2 − 1)) ≈ 0.812. Our analysis unveils a subtle interplay of the clustering transition with the rigidity (naive reconstruction) threshold that occurs on the same asymptotic scale at γ r = 1. 4.3 Reweighted probability distributions 19 4.4 Numerical resolution 22 4.5 The fixed point equation and the determination of γ d 25 4.6 An analytic lowerbound on γ d 28 5 Conclusion 29