We show that the twin-width of every $n$-vertex $d$-regular graph is at most $n^{\frac{d-2}{2d-2}+o(1)}$ and that almost all $d$-regular graphs attain this bound. More generally, we obtain bounds on the twin-width of sparse Erd\H{o}s-Renyi and regular random graphs, complementing the bounds in the denser regime due to Ahn, Chakraborti, Hendrey, Kim and Oum.

翻译：我们证明了每个 $n$ 顶点 $d$ 正则图的孪生宽度至多为 $n^{\frac{d-2}{2d-2}+o(1)}$，并且几乎所有 $d$ 正则图均达到此上界。更一般地，我们得到了稀疏 Erdős–Renyi 随机图与正则随机图的孪生宽度界，这补充了 Ahn、Chakraborti、Hendrey、Kim 与 Oum 在较稠密情形下的界。