We prove that whenever $d=d(n)\to\infty$ and $n-d\to\infty$ as $n\to\infty$, then with high probability for any non-trivial initial colouring, the colour refinement algorithm distinguishes all vertices of the random regular graph $\mathcal{G}_{n,d}$. This, in particular, implies that with high probability $\mathcal{G}_{n,d}$ admits a canonical labelling computable in time $O(\min\{n^ω,nd^2+nd\log n\})$, where $ω<2.372$ is the matrix multiplication exponent.

翻译：我们证明，当$d=d(n)\to\infty$且$n-d\to\infty$在$n\to\infty$时成立时，对于任意非平凡的初始着色，着色细化算法以高概率能够区分随机正则图$\mathcal{G}_{n,d}$的所有顶点。这尤其意味着，以高概率$\mathcal{G}_{n,d}$存在一个可在$O(\min\{n^ω,nd^2+nd\log n\})$时间内计算的规范标号，其中$ω<2.372$为矩阵乘法指数。