2026/04/30 by Mikio Kano, Shun-ichi Maezawa, Akira Saito +1
Mathematics · #math.CO
arxiv created 2026/08/03 · arxiv updated 2026/08/04
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 λ-edge-connected r-regular hypergraph \HH with k|V(\HH)| 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 \HH for hypergraphs and that it is stronger than the classical upper bound based on the edge-connectivity in most cases.