Scramble number and tree-cut decompositions
L Cenek, L Ferguson, E Gebre, C Marcussen… - arXiv preprint arXiv …, 2022 - arxiv.org
The scramble number of a graph is an invariant recently developed to study chip-firing
games and divisorial gonality. In this paper we introduce the screewidth of a graph, based …
games and divisorial gonality. In this paper we introduce the screewidth of a graph, based …
Bounding the number of graph refinements for Brill-Noether existence
K Christ, Q Ma - arXiv preprint arXiv:2304.07405, 2023 - arxiv.org
Let $ G $ be a finite graph of genus $ g $. Let $ d $ and $ r $ be non-negative integers such
that the Brill-Noether number is non-negative. It is known that for some $ k $ sufficiently …
that the Brill-Noether number is non-negative. It is known that for some $ k $ sufficiently …
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 …
Fibonacci Sumsets and the Gonality of Strip Graphs
D Jensen, DR Laboy - arXiv preprint arXiv:2408.09247, 2024 - arxiv.org
We provide a new perspective on the divisor theory of graphs, using additive combinatorics.
As a test case for this perspective, we compute the gonality of certain families of outerplanar …
As a test case for this perspective, we compute the gonality of certain families of outerplanar …
[PDF][PDF] Divisorial gonality of graphs, the slice rank polynomial method, and tensor products of convex cones
JD de Bruyn - 2023 - research.tudelft.nl
Divisorial gonality of graphs, the slice rank polynomial method, and tensor products of
convex cones Page 1 Delft University of Technology Divisorial gonality of graphs, the slice …
convex cones Page 1 Delft University of Technology Divisorial gonality of graphs, the slice …
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 …