{
  "id": "2212.06109",
  "version": "v1",
  "published": "2022-12-12T18:32:04.000Z",
  "updated": "2022-12-12T18:32:04.000Z",
  "title": "Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings",
  "authors": [
    "Vishesh Jain",
    "Huy Tuan Pham"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO",
    "cs.DM",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-12T18:32:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "steiner triple systems",
      "latin square",
      "edge colorings",
      "optimal thresholds",
      "proper list edge-colorings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}