We show that the threshold for having a rainbow copy of a power of a Hamilton cycle in a randomly edge colored copy of is within a constant factor of the uncolored threshold. Our proof requires times the minimum number of colors.

中文翻译：

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Gn,p 中汉密尔顿循环的彩虹幂

我们证明了在随机边缘彩色副本中拥有汉密尔顿循环幂的彩虹副本的阈值$G_{n,p}$在未着色阈值的恒定因子内。我们的证明要求$（1+\epsilon ）$乘以最小颜色数。