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arXiv · 2212.06109

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

Vishesh Jain·Huy Tuan Pham
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Abstract

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 $Θ(\log{n}/n)$. 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.

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Vishesh Jain, Huy Tuan Pham. 2022-12-19. Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings. https://arxiv.org/abs/2212.06109

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