We show that every k-uniform hypergraph on n vertices whose minimum $(k-2)$-degree is at least $(5/9+o(1))n^2/2$ contains a Hamiltonian cycle. A construction due to Han and Zhao shows that this minimum degree condition is optimal. The same result was proved independently by Lang and Sanhueza-Matamala.

中文翻译：

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具有密集链接图的超图中的哈密顿环

我们显示n个顶点上的每个k均匀超图的最小值$（ķ-\mathrm{2个}）$-度至少 $（5/9+Ø（\mathrm{1个}））{ñ}^{\mathrm{2个}}/\mathrm{2个}$包含哈密顿循环。Han和Zhao的构造表明此最小度条件是最佳的。Lang和Sanhueza-Matamala独立证明了相同的结果。