Decomposing hypergraphs into simple hypertrees (Q1586356)

Let \(T\) be a simple \(k\)-uniform hypertree with \(t\) edges. The author proves that if \(H\) is any \(k\)-uniform hypergraph with \(n\) vertices and with minimum degree at least \[ \frac{n^{k-1}}{2^{k-1}(k-1)!} (1+o(1)), \] and the number of edges of \(H\) is a multiple of \(t\) then \(H\) has a \(T\)-decomposition. Moreover, the author gives some open problems.