The equitable list tree-coloring model is an useful tool to formulate a structure decomposition problem on the complex network with some security considerations. In this paper, it is proved that the equitable list vertex arboricity of every graph with treewidth ω is at most $\lceil \mathrm{\Delta }(G)/2\rceil +\omega -2$ whenever $\mathrm{\Delta }(G)\ge 4\omega +1$, and moreover, if such a graph does not contain $K_{3,3}$ as a topological minor, then its equitable list vertex arboricity is at most $\lceil \mathrm{\Delta }(G)/2\rceil$ provided that $\omega \in \{2,3,4\}$ and $\mathrm{\Delta }(G)\ge 6\omega -3$.

中文翻译：

---

有界树宽图的公平列表树着色

公平列表树着色模型是一个有用的工具，可以在考虑安全性的前提下制定复杂网络上的结构分解问题。本文证明了每个树宽为ω的图的等价列表顶点的树状度最大$\lceil \mathrm{\Delta }（G）/2\rceil +\omega -2$ 每当 $\mathrm{\Delta }（G）\ge 4\omega +\mathrm{1个}$，此外，如果此类图表不包含 ${ķ}_{3，3}$ 作为拓扑未成年人，那么其等价列表顶点的树状度最多 $\lceil \mathrm{\Delta }（G）/2\rceil$ 规定 $\omega \in \{2，3，4\}$ 和 $\mathrm{\Delta }（G）\ge 6\omega -3$。