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arXiv · 2204.03964

Threshold for Steiner triple systems

Ashwin Sah·Mehtaab Sawhney·Michael Simkin
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Abstract

We prove that with high probability $\mathbb{G}^{(3)}(n,n^{-1+o(1)})$ contains a spanning Steiner triple system for $n\equiv 1,3\pmod{6}$, 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.

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Ashwin Sah, Mehtaab Sawhney, Michael Simkin. 2022-05-03. Threshold for Steiner triple systems. https://arxiv.org/abs/2204.03964

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