2026/07/17 by Hongliang Lu, Yan Wang, Feihong Yuan
#math.CO
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.