Stable Divisorial Gonality is in NP

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

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

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 publicationTHEORY AND PRACTICE OF COMPUTER SCIENCE, SOFSEM 2019
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
Pages81-93
Number of pages13
ISBN (Electronic)978-3-030-10801-4
ISBN (Print)978-3-030-10800-7
DOIs
Publication statusPublished - 2019

Publication series

SeriesLecture Notes in Computer Science
Volume11376
ISSN0302-9743

Keywords

  • CURVES

Cite this