Berge $k$-Factors of Regular Hypergraphs

A Berge $k$-factor in a hypergraph is a generalization of a $k$-factor in a graph. In this paper, we study the problem of determining the values $k$ such that every $\lambda$-edge-connected $r$-regular hypergraph $\text{HH}$ with $k\mathrm{\mid }V(\text{HH})\mathrm{\mid }$ even has a Berge $k$-factor. While this problem is completely solved for ordinary graphs, we report that there arises a new upper bound to $k$ based on the rank of $\text{HH}$ for hypergraphs and that it is stronger than the classical upper bound based on the edge-connectivity in most cases.