Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings

12/12/2022

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by   Vishesh Jain, et al.

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We show that the threshold for the binomial random 3-partite, 3-uniform hypergraph G^3((n,n,n),p) to contain a Latin square is Θ(logn/n). We also prove analogous results for Steiner triple systems and proper list edge-colorings of the complete (bipartite) graph with random lists. Our results answer several related questions of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus.