Stable Divisorial Gonality is in NP

H.L. Bodlaender, Marieke van der Wegen, Tom van der Zanden

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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, 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 number of subdivisions needed for minimum stable divisorial gonality of a graph with n vertices is bounded by 2p(n) for a polynomial p.
Original languageEnglish
Title of host publicationSOFSEM 2019: Theory and Practice of Computer Science
Subtitle of host publication45th International Conference on Current Trends in Theory and Practice of Computer Science, Nový Smokovec, Slovakia, January 27-30, 2019, Proceedings
EditorsBarbara Catania, Rastislav Královic, Jerzy Nawrocki, Giovanni Pighizzini
PublisherSpringer, Cham
ISBN (Electronic)978-3-030-10801-4
ISBN (Print)978-3-030-10800-7
Publication statusPublished - 2019

Publication series

SeriesLecture Notes in Computer Science

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