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 …
On the gonality of Cartesian products of graphs
I Aidun, R Morrison - arXiv preprint arXiv:1909.10421, 2019 - arxiv.org
In this paper we study Cartesian products of graphs and their divisorial gonality, which is a
tropical version of the gonality of an algebraic curve. We present an upper bound on the …
tropical version of the gonality of an algebraic curve. We present an upper bound on the …
Gonality sequences of graphs
I Aidun, F Dean, R Morrison, T Yu, J Yuan - SIAM Journal on Discrete …, 2021 - SIAM
We associate to any graph a sequence of integers called the gonality sequence of the
graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is …
graph, consisting of the minimum degrees of divisors of increasing rank on the graph. This is …
Chip firing and algebraic curves
D Jensen - Notices Amer. Math. Soc, 2021 - ams.org
The chip firing game is played with poker chips on the vertices of a graph. Though
seemingly simple, this game has deep connections to various fields of mathematics. In this …
seemingly simple, this game has deep connections to various fields of mathematics. In this …
Divisorial and geometric gonality of higher-rank tropical curves
JD de Bruyn, D Holmes, D van der Vorm - arXiv preprint arXiv:2112.04205, 2021 - arxiv.org
We consider a variant of metrised graphs where the edge lengths take values in a
commutative monoid, as a higher-rank generalisation of the notion of a tropical curve …
commutative monoid, as a higher-rank generalisation of the notion of a tropical curve …