We study rainbow-free colourings of k-uniform hypergraphs; that is, colourings that use k colours but with the property that no hyperedge attains all colours. We show that $p^{⁎}=(k-1)(\ln n)/n$ is the threshold function for the existence of a rainbow-free colouring in a random k-uniform hypergraph.

中文翻译：

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关于均匀超图的无彩虹着色

我们研究k均匀超图的无彩虹着色；也就是说，使用k种颜色但具有没有超边达到所有颜色的属性的着色。我们证明${磷}^{⁎}=(克-1)(\mathrm{输入}n)/n$是随机k均匀超图中存在无彩虹着色的阈值函数。