On the scramble number of graphs
Combinatorics
2021-12-09 v3 Algebraic Geometry
Abstract
The scramble number of a graph is an invariant recently developed to aid in the study of divisorial gonality. In this paper we prove that scramble number is NP-hard to compute, also providing a proof that computing gonality is NP-hard even for simple graphs, as well as for metric graphs. We also provide general lower bounds for the scramble number of a Cartesian product of graphs, and apply these to compute gonality for many new families of product graphs.
Keywords
Cite
@article{arxiv.2103.15253,
title = {On the scramble number of graphs},
author = {Marino Echavarria and Max Everett and Robin Huang and Liza Jacoby and Ralph Morrison and Ben Weber},
journal= {arXiv preprint arXiv:2103.15253},
year = {2021}
}
Comments
20 pages, 6 figures