Decompositions of hypergraphs into hyperstars (Q1106243)

P(X) (respectively \(P_ n(X))\) denotes the set of non-empty subsets (respectively n-element subsets) of a set X. A hyperstar with center F and size c is a hypergraph (X,E) such that \(F\subseteq \cap E\) and \(| E| =c\). A decomposition of a hypergraph \(H=(X,E)\) is a set of hypergraphs on set X whose edge sets form a partition of E. In this paper necessary and sufficient conditions are given for the existence of a decomposition of a hypergraph into hyperstars with given centers and sizes. These results are then applied to obtain sufficient conditions for the existence of a hyperstar decomposition of the hypergraphs (X,P(X)) and \((X,P_ n(X))\).