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arXiv · 2607.15671

Perfect matching in 4-partite 4-uniform hypergraphs

Hongliang Lu·Yan Wang·Feihong Yuan
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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 Markstr\"om (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.

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Hongliang Lu, Yan Wang, Feihong Yuan. 2026-07-17. Perfect matching in 4-partite 4-uniform hypergraphs. https://arxiv.org/abs/2607.15671

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