An algorithmic framework for obtaining lower bounds for random Ramsey problems

In the second part of the paper we apply this framework to address and solve various open problems. In particular, we extend the result of Bohman, Frieze, Pikhurko and Smyth (2010) for bounded anti-Ramsey problems in random graphs to the case of 2 colors and to hypergraph cliques. As a corollary, this proves a matching lower bound for the result of Friedgut, Rödl and Schacht (2010) and, independently, Conlon and Gowers (2016) for the classical Ramsey problem for hypergraphs in the case of cliques. Finally, we provide matching lower bounds for a proper-coloring version of anti-Ramsey problems introduced by Kohayakawa, Konstadinidis and Mota (2014) in the case of cliques and cycles.