acyclic decomposition of hypergraphs The following is from the paper _Arboricity: An acyclic hypergraph decomposition problem motivated by database theory_ by Yeow Meng Chee, Lijun Ji, Andrew Lim, Anthony K.H. Tung: ![enter image description here]( ![enter image description here]( **Question:** For an arbitrary finite hypergraph $\mathcal{H}$, does $\mathcal{H}$ always have a finite acyclic decomposition? Are there any references?

For an arbitrary finite hypergraph $\mathcal{H}$ put each edge in a separate component, that is, take $\mathcal{A}_i = \\{A_i\\}$. All such one-hyperedge graphs have all degrees equal to one, so they are acyclic.

I hope this helps $\ddot\smile$