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

Vishesh Jain; Huy Tuan Pham

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

Combinatorics 2022-12-20 v2 Discrete Mathematics Probability

Authors: Vishesh Jain , Huy Tuan Pham

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 $\Theta(\log{n}/n)$ . 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-H\"aggkvist, Simkin, and Kang-Kelly-K\"uhn-Methuku-Osthus.

Keywords

latin squares steiner triple systems edge colorings random hypergraphs thresholds binomial random models

Cite

@article{arxiv.2212.06109,
  title  = {Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings},
  author = {Vishesh Jain and Huy Tuan Pham},
  journal= {arXiv preprint arXiv:2212.06109},
  year   = {2022}
}

Comments

10 pages. Simplified proof; results unchanged

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

Abstract

Keywords

Cite

Comments

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