Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth at most 8" by "simple treewidth at most 6".

中文翻译：

---

一种改进的平面图积结构定理

Dujmovi\'c、Joret、Micek、Morin、Ueckerdt 和 Wood [J. ACM 2020] 证明对于每个平面图 $G$ 都有一个图 $H$ 树宽至多为 8 和路径 $P$ 使得 $G\subseteq H\boxtimes P$。我们通过用“简单的树宽最多 6”替换“树宽最多 8”来改进这个结果。