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 …

This paper compares the divisorial gonality of a finite graph G to the divisorial gonality of the
associated metric graph Γ (G, 1) with unit lengths. We show that dgon (Γ (G, 1)) is equal to …

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 …

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 …

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 …

Abstract We study Brill–Noether existence on a finite graph using methods from polyhedral
geometry and lattices. We start by formulating analogues of the Brill–Noether conjectures …

We analyze a family of graphs known as banana graphs, with two marked vertices, through
the lens of Hurwitz-Brill-Noether theory. As an application, we construct explicit new …

We give a proof of the combinatorial Brill-Noether conjecture for cactus graphs. This
conjecture was formulated by Baker in 2008 when studying the interaction between …