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Stable Divisorial Gonality is in NP
Theory of Computing Systems ( IF 0.6 ) Pub Date : 2020-12-07 , DOI: 10.1007/s00224-020-10019-4
Hans L. Bodlaender , Marieke van der Wegen , Tom C. van der Zanden

Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph G can be defined with help of a chip firing game on G. The stable divisorial gonality of G is the minimum divisorial gonality over all subdivisions of edges of G. In this paper we prove that deciding whether a given connected graph has stable divisorial gonality at most a given integer k belongs to the class NP. Combined with the result that (stable) divisorial gonality is NP-hard by Gijswijt et al., we obtain that stable divisorial gonality is NP-complete. The proof consists of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the total number of subdivisions needed for minimum stable divisorial gonality of a graph with m edges is bounded by mO(mn).



中文翻译:

NP的稳定除数公有性

除数角和稳定除数角是图参数,它们起源于代数几何。可以借助G上的筹码射击游戏来定义连通图G的除角度。的稳定divisorial gonality ģ结束的边缘的所有子的最小divisorial gonality ģ。在本文中,我们证明了确定给定连通图最多在给定整数k下是否具有稳定的除数对角性属于NP类。结合Gijswijt等人的(稳定)除数角为NP-hard的结果,我们得出稳定的除数角为NP-complete。该证明包括部分证书,可以通过求解整数线性编程实例来对其进行验证。作为推论,我们具有m边的图的最小稳定除数角度所需的细分总数由m Om n界定。

更新日期:2020-12-08
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