A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \( Δ\) when the number of colors is greater than \( 3.637 Δ+ 1\).

翻译：本文提出了一种从图的所有正确着色中精确采样的新算法。这是首个在颜色数大于 \( 3.637 Δ+ 1\) 时，其期望运行时间被严格保证为关于最大度为 \( Δ\) 的图规模呈线性增长的此类算法。