Threshold for Steiner triple systems.

We prove that with high probability G (3) (n , n - 1 + o (1)) contains a spanning Steiner triple system for n ≡ 1 , 3 (mod 6) , establishing the exponent for the threshold probability for existence of a Steiner triple system. We also prove the analogous theorem for Latin squares. Our result follows from a novel bootstrapping scheme that utilizes iterative absorption as well as the connection between thresholds and fractional expectation-thresholds established by Frankston, Kahn, Narayanan, and Park. [ABSTRACT FROM AUTHOR]