For a given $n$, is there a way to calculate the minimal value $m$ such that you can decompose the multigraph:
$$m \times K_n$$
into disjoint 3-cycles?
What about a more general result applied to multihypergraphs?
Say you have a hypergraph $H$ over $n$ vertices which contains all hyperedges of size $t \ge 2$. For a given $k > t$, is there a way to calculate the smallest $m$ such that you can decompose the multihypergraph consisting of the hyperedges of $H$ repeated $m$ times into $k$-cliques (apologies if my terminology is wrong) of hyperedges?
For example, if $t = 3$ and $k = 5$, one 5-clique in the decomposition might be:
$$\{1, 2, 3\}, \{1, 2, 4\}, \{1, 2, 5\}, \{1, 3, 4\}, \{1, 3, 5\}$$ $$\{1, 4, 5\}, \{2, 3, 4\}, \{2, 3, 5\}, \{2, 4, 5\}, \{3, 4, 5\}$$
