The volume and foundation of star trades

Abstract

An x-star trade consists of two disjoint decompositions of some simple graph H into copies of $K_{1,x}$, the graph known as the x-star. The number of vertices of H is referred to as the foundation of the trade, while the number of copies of $K_{1,x}$ in each of the decompositions is called the volume of the trade. We determine all values of x, $v$ and s for which there exists a $K_{1,x}$-trade of volume s and foundation $v$.