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Perfect Matchings in Random k-Partite k-Uniform Hypergraphs
The question of finding the threshold for perfect matchings in random k-uniform hypergraphs dates back to at least 1981, when “Shamir’s problem” first appeared in print. The threshold was identified by Johansson, Kahn, and Vu in 2008. This result was improved with Kahn’s proof of the sharp threshold in 2019, involving careful and creative applications of common techniques in probabilistic combinatorics and random graphs. In this dissertation, we extend and expound upon Kahn’s work to find the sharp threshold for perfect matchings in a related random hypergraph model: random hypergraphs that are both k-uniform and k-partite. We show that the sharp threshold in this model (on a hypergraph with kn vertices) is n ln(n) edges.
Pai, Leilani, "Perfect Matchings in Random k-Partite k-Uniform Hypergraphs" (2023). ETD collection for University of Nebraska - Lincoln. AAI30575940.