Berge $k$-Factors of Regular Hypergraphs

TL;DR

This paper investigates conditions for the existence of Berge $k$-factors in regular hypergraphs, revealing a new upper bound based on hypergraph rank that surpasses classical bounds.

Contribution

It introduces a new upper bound for Berge $k$-factors in hypergraphs, extending known graph results to hypergraph settings.

Findings

New upper bound for $k$ based on hypergraph rank

Stronger than classical edge-connectivity bounds in most cases

Complete solution for graphs does not directly extend to hypergraphs

Abstract

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 $\HH$ 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.