Berge $k$-Factors of Regular Hypergraphs
Combinatorics
2026-05-14 v2
Abstract
A Berge -factor in a hypergraph is a generalization of a -factor in a graph. In this paper, we study the problem of determining the values such that every -edge-connected -regular hypergraph with even has a Berge -factor. While this problem is completely solved for ordinary graphs, we report that there arises a new upper bound to based on the rank of for hypergraphs and that it is stronger than the classical upper bound based on the edge-connectivity in most cases.
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}
}