论文标题
拉丁正方形，施泰纳三重系统和边缘色的最佳阈值
Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings
论文作者
论文摘要
我们表明，包含拉丁正方形的二项式随机$ 3 $ - 明确的阈值，$ 3 $ - 均匀的超图$ g^{3}（（n，n，n，n），p）$是$θ（\ log {n}/n）$。我们还证明了Steiner Triple Systems的类似结果和完整（两部分）图的正确列表边彩色，并带有随机列表。我们的结果回答了Johansson，Luria-Simkin，Casselgren-Häggkvist，Simkin和Kang-Kelly-kühn-Methuku-Osthus的几个相关问题。
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.
