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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27483 |
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| _version_ | 1866913121763852288 |
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| author | Kano, Mikio Maezawa, Shun-ichi Saito, Akira Yoshimoto, Kiyoshi |
| author_facet | Kano, Mikio Maezawa, Shun-ichi Saito, Akira Yoshimoto, Kiyoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27483 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Berge $k$-Factors of Regular Hypergraphs Kano, Mikio Maezawa, Shun-ichi Saito, Akira Yoshimoto, Kiyoshi Combinatorics 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. |
| title | Berge $k$-Factors of Regular Hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.27483 |