Bounds on higher graph gonality
Combinatorics
2022-06-15 v1 Algebraic Geometry
Abstract
We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving independence number, and lower bounds on gonality by scramble number. We apply our bounds to study the computational complexity of computing higher gonalities, proving that it is NP-hard to compute the second gonality of a graph when restricting to multiplicity-free divisors.
Keywords
Cite
@article{arxiv.2206.06907,
title = {Bounds on higher graph gonality},
author = {Lisa Cenek and Lizzie Ferguson and Eyobel Gebre and Cassandra Marcussen and Jason Meintjes and Ralph Morrison and Liz Ostermeyer and Shefali Ramakrishna},
journal= {arXiv preprint arXiv:2206.06907},
year = {2022}
}
Comments
14 pages, 5 figures