Decomposing uniform hypergraphs into uniform hypertrees and single edges

Given two r-uniform hypergraphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a hypergraph isomorphic to H. Let phi(r)(n, H) be the smallest integer such that any r-uniform hypergraph G of order n admits an H-decomposition with at most phi(r)(n, H) parts. In this paper we determine the exact value of phi(r)(n, H) when H is an arbitrary r-uniform hypertree with t edges. (C) 2021 Elsevier B.V. All rights reserved.