On the decomposition of random hypergraphs

For an r-uniform hypergraph H, let f(H) be the minimum number of complete r-partite r-uniform subhypergraphs of H whose edge sets partition the edge set of H. In this talk, I will discuss the value of f(H) for the random hypergraph H. Namely, I will prove that if (log n)/n ≤ p ≤ 1/2 and H ∈ H(n, p), then with high probability f(H) = (1− π(K(r−1) r ) + o(1)) ( n r−1 ) , where π(K(r−1) r ) is the Turán density of K (r−1) r . Tuesday, June 2, 2015 4:00 PM AP&M 7421 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *