We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9+o(1))n^2/2$ contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal.

中文翻译：

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4-均匀超图中紧哈密顿循环的最小对度条件

我们表明，每个具有 $n$ 个顶点和最小对度至少 $(5/9+o(1))n^2/2$ 的 4-uniform 超图都包含一个紧密的哈密顿循环。这个度条件是渐近最优的。