For $\textbf{ r}=(r_1,\ldots,r_k)$, an $\textbf{ r}$-factorization of the complete $\lambda$-fold $h$-uniform $n$-vertex hypergraph $\lambda K_n^h$ is a partition of the edges of $\lambda K_n^h$ into $F_1,\ldots, F_k$ such that $F_j$ is $r_j$-regular and spanning for $1\leq j\leq k$. This paper shows that for $n>\frac{ m-1}{ 1-2^{ \frac{ 1}{ 1-h}}}+h-1$, a partial $\textbf{ r}$-factorization of $\lambda K_m^h$ can be extended to an $\textbf{ r}$-factorization of $\lambda K_n^h$ if and only if the obvious necessary conditions are satisfied.
Categories: math.CO