MIT-Harvard-MSR Combinatorics Seminar

Wednesday, December 07, 2022 at 4:15pm to 5:15pm

MIT-Math Dept., MIT-Building 2, Room 132

Speaker:  Huy Tuan Pham  (Standord University)

Title:  Thresholds for Latin squares and Steiner triple systems


We show that if each edge of the complete bipartite graph Kn,n is given a random list of C(\log n) colors among n colors, then with high probability, there is a proper edge coloring where the color of each edge comes from the corresponding list. In other words, a random 3-partite 3-uniform hypergraph with parts of size n and edge density C(\log n)/n contains a Latin square with high probability. This resolves a conjecture of Luria and Simkin on threshold for containment of a Latin square, and the related conjecture of Simkin on threshold for containment of a Steiner triple system. Based on joint work with Vishesh Jain.

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