2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223391We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary constraint satisfaction problems with domain size three.CombinatoricsProbability05C80text