English

Berge $k$-Factors of Regular Hypergraphs

Combinatorics 2026-05-14 v2

Abstract

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

Keywords

Cite

@article{arxiv.2604.27483,
  title  = {Berge $k$-Factors of Regular Hypergraphs},
  author = {Mikio Kano and Shun-ichi Maezawa and Akira Saito and Kiyoshi Yoshimoto},
  journal= {arXiv preprint arXiv:2604.27483},
  year   = {2026}
}
R2 v1 2026-07-01T12:42:59.319Z