Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles

Abstract

It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order $v$ if and only if $v \equiv 0, 1,\text{ or }2\ (\operatorname{mod} 9)$. For all positive integers $\lambda$ and $v$, we find a maximum packing with loose 3-cycles of the $\lambda$-fold complete 3-uniform hypergraph of order $v$. We show that, if $v \geq 6$, such a packing has a leave of two or fewer edges.