SIAM Journal on Discrete Mathematics, Volume 35, Issue 2, Page 814-839, January 2021.
We associate to any graph a sequence of integers called the gonality sequence of the graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is a tropical analogue of the gonality sequence of an algebraic curve. We study gonality sequences for graphs of low genus, proving that for genus up to 5, the gonality sequence is determined by the genus and the first gonality. We then prove that any reasonable pair of the first two gonalities is achieved by some graph. We also develop a modified version of Dhar's burning algorithm more suited for studying higher gonalities.

中文翻译：

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图的有向性序列

SIAM Journal on Discrete Mathematics，第 35 卷，第 2 期，第 814-839 页，2021 年 1 月。
我们将一个整数序列与任何图相关联，称为图的共性序列，由图上递增秩的除数的最小度数组成. 这是代数曲线的共性序列的热带模拟。我们研究了低属图的gonality序列，证明对于5个以下的属，gonality序列由属和第一个gonality决定。然后我们证明前两个方向的任何合理对都是通过某个图实现的。我们还开发了 Dhar 燃烧算法的修改版本，更适合研究更高的定性。