Threshold for Steiner triple systems

Ashwin Sah, Mehtaab Sawhney, Michael Simkin

We prove that with high probability ${\mathbb{G}}^{(3)}(n,n^{-1+o(1)})$ contains a spanning Steiner triple system for $n\equiv 1,3(\mathrm{mod}6)$, establishing the exponent for the thresho…