On the scramble number of graphs
M Echavarria, M Everett, R Huang, L Jacoby… - Discrete Applied …, 2022 - Elsevier
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 …
divisorial gonality. In this paper we prove that scramble number is NP-hard to compute, also …
Chip-firing on the Platonic solids: a primer for studying graph gonality
M Beougher, K Ding, M Everett, R Huang, C Lee… - arXiv preprint arXiv …, 2024 - arxiv.org
This paper provides a friendly introduction to chip-firing games and graph gonality. We use
graphs coming from the five Platonic solids to illustrate different tools and techniques for …
graphs coming from the five Platonic solids to illustrate different tools and techniques for …
On the semigroup of graph gonality sequences
A Fessler, D Jensen, E Kelsey, N Owen - arXiv preprint arXiv:2306.11118, 2023 - arxiv.org
The $ r $ th gonality of a graph is the smallest degree of a divisor on the graph with rank $ r
$. The gonality sequence of a graph is a tropical analogue of the gonality sequence of an …
$. The gonality sequence of a graph is a tropical analogue of the gonality sequence of an …
Computing higher graph gonality is hard
R Morrison, L Tolley - arXiv preprint arXiv:2208.03573, 2022 - arxiv.org
In the theory of divisors on multigraphs, the $ r^{th} $ divisorial gonality of a graph is the
minimum degree of a rank $ r $ divisor on that graph. It was proved by Gijswijt et al. that the …
minimum degree of a rank $ r $ divisor on that graph. It was proved by Gijswijt et al. that the …
Multiplicity-free gonality on graphs
F Dean, M Everett, R Morrison - arXiv preprint arXiv:2107.12955, 2021 - arxiv.org
The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that
graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration …
graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration …
[PDF][PDF] Gonality Sequences of Multipartite Graphs
M Xu - 2022 - math.mit.edu
In this paper, we deal with a particular sequence associated with a graph, the gonality
sequence. This gonality sequence is a part of a larger topic of the chipfiring game on a …
sequence. This gonality sequence is a part of a larger topic of the chipfiring game on a …