7 papers · 1 filter
The -gonal locus in the moduli space of tropical plane curves
Desmond Leitz, Ralph Morrison, Søren Newman-Taylor +1
We introduce and study the locus of genus tropical plane curves of gonality inside the moduli space of tropica…
Chip-Firing Games on Banana Trees
Marchelle Beougher, Nila Cibu, Kexin Ding +6
We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomia…
The tropical crossing number of a finite graph
Noah Cape, Ralph Morrison
In 2015, Cartwright et al. showed that any -regular metric graph arises as the skeleton of a tropical plane curve with nodes allowed. They introduced the tropical crossing numbe…
The gonality of circulant graphs
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre +5
The gonality of a graph measures how difficult it is to move chips around the entirety of a graph according to certain chip-firing rules without introducing debt. In this paper we…
The gonality of chess graphs
Nila Cibu, Kexin Ding, Steven DiSilvio +4
Chess graphs encode the moves that a particular chess piece can make on an chessboard. We study through these graphs through the lens of chip-firing games and graph gon…
The Gonality of Queen's Graphs
Ralph Morrison, Noah Speeter
In this paper we study queen's graphs, which encode the moves by a queen on an chess board, through the lens of chip-firing games. We prove that their gonality is equal…
On the size and complexity of scrambles
Seamus Connor, Steven DiSilvio, Sasha Kononova +2
The scramble number of a graph, a natural generalization of bramble number, is an invariant recently developed to study chip-firing games and graph gonality. We introduce the carto…