In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most k, when an effective divisor of degree k that reaches all vertices is given. We also give a similar result for two related notions: stable divisorial gonality and stable gonality.

中文翻译：

---

构造有界共性图的树分解

在本文中，我们给出了一个图的树宽至多是它的除数共性这一事实的建设性证明。证明给出了一个多项式时间算法来构造宽度最大为k的树分解，当给出到达所有顶点的k度的有效除数时。我们还对两个相关概念给出了类似的结果：稳定除数共性和稳定共性。