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.
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 language | English |
---|---|
Title of host publication | THEORY AND PRACTICE OF COMPUTER SCIENCE, SOFSEM 2019 |
Subtitle of host publication | 45th International Conference on Current Trends in Theory and Practice of Computer Science, Nový Smokovec, Slovakia, January 27-30, 2019, Proceedings |
Editors | Barbara Catania, Rastislav Královic, Jerzy Nawrocki, Giovanni Pighizzini |
Publisher | Springer, Cham |
Pages | 81-93 |
Number of pages | 13 |
ISBN (Electronic) | 978-3-030-10801-4 |
ISBN (Print) | 978-3-030-10800-7 |
DOIs | |
Publication status | Published - 2019 |
Publication series
Series | Lecture Notes in Computer Science |
---|---|
Volume | 11376 |
ISSN | 0302-9743 |
Keywords
- CURVES