Computing graph gonality is hard
Abstract
There are several notions of gonality for graphs. The divisorial gonality dgon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. The stable gonality sgon(G) of a graph G is the minimum degree of a finite harmonic morphism from a refinement of G to a tree, as defined by Cornelissen, Kato and Kool. We show that computing dgon(G) and sgon(G) are NP-hard by a reduction from the maximum independent set problem and the vertex cover problem, respectively. Both constructions show that computing gonality is moreover APX-hard.
Keywords
Cite
@article{arxiv.1504.06713,
title = {Computing graph gonality is hard},
author = {Dion Gijswijt and Harry Smit and Marieke van der Wegen},
journal= {arXiv preprint arXiv:1504.06713},
year = {2019}
}
Comments
The previous version only dealt with hardness of the divisorial gonality. The current version also shows hardness of stable gonality and discusses the relation between the two graph parameters