A Randomized Version of Ramseyʼs Theorem

For every integer r ⩾ 2 we call a k-uniform hypergraph H on n vertices r-Ramsey-forcing if every r-edge-coloring of the underlying complete graph K n contains a monochromatic copy of K k such that its vertices form an edge in H. In this work we determine the threshold for a random k-uniform hypergraph with n vertices to be r-Ramsey-forcing. This settles an open question from Allen, Böttcher, Hladký, and Piguet [Allen, P., J. Böttcher, J. Hladký and D. Piguet, Turánnical hypergraphs, arXiv:1011.1483v1].