We prove that a random graph , with p above the Hamiltonicity threshold, is typically such that for any r-coloring of its edges there exists a Hamilton cycle with at least edges of the same color. This estimate is asymptotically optimal.

中文翻译：

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随机图中的颜色偏差汉密尔顿循环

我们证明了 p 高于哈密顿性阈值的随机图通常使得对于其边缘的任何r着色，都存在一个至少具有相同颜色边缘的哈密顿循环。这个估计是渐近最优的。