稳定gonality是可计算的
Stable gonality is computable
AI总结：
本文证明了判定图的稳定gonality是否不超过给定整数属于NP类，并给出了时间复杂度为$O((1.33n)^nm^m \text{poly}(n,m))$的计算算法。
摘要：
稳定gonality是一个衡量多重图复杂度的参数，它通过映射到树来定义。这些映射在某种意义上将边均匀地分配到树的边上；稳定gonality要求找到使得映射到树的每条边上的边数最少的映射。该参数与树宽相关，但与树宽不同，它能区分多重图及其底层简单图。稳定gonality对数论中的问题具有重要意义。在本文中，我们证明了判定给定图的稳定gonality是否至多为给定整数$k$属于NP类，并给出了一种在$O((1.33n)^nm^m \text{poly}(n,m))$时间内计算图的稳定gonality的算法。
英文摘要：
Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the minimum number of edges mapped to each edge of the tree. This parameter is related to treewidth, but unlike treewidth, it distinguishes multigraphs from their underlying simple graphs. Stable gonality is relevant for problems in number theory. In this paper, we show that deciding whether the stable gonality of a given graph is at most a given integer $k$ belongs to the class NP, and we give an algorithm that computes the stable gonality of a graph in $O((1.33n)^nm^m \text{poly}(n,m))$ time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
