Year: 2026
Type: preprint
Abstract: A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph such that every edge intersects each partition class in exactly one vertex, where each partition class has size $n$. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings in balanced \(3\)-partite \(3\)-graphs. In this paper, we determine the minimum vertex-degree threshold for balanced \(4\)-partite \(4\)-graphs. The proof relies on a reduction framework for \(k\)-partite \(k\)-graphs, through which the existence of a perfect fractional matching is converted into a finite-dimensional optimization problem.
Source: arXiv (Cornell University)
Authors: Lu, Hongliang, Wang, Yan, Yuan, Feihong
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4716027175, G7160286548
OpenAlex ID: W7169807437
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