39 citations · 73 across the 20 of their papers we have counts for
29 papers
Graphs of scramble number two
Robin Eagleton, Ralph Morrison
The scramble number of a graph provides a lower bound for gonality and an upper bound for treewidth, making it a graph invariant of interest. In this paper we study graphs of scram…
Scramble number and tree-cut decompositions
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre +6
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 on…
Computing higher graph gonality is hard
Ralph Morrison, Lucas Tolley
In the theory of divisors on multigraphs, the divisorial gonality of a graph is the minimum degree of a rank divisor on that graph. It was proved by Gijswijt et al. th…
Bounds on higher graph gonality
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre +5
We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalit…
Uniform scrambles on graphs
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre +5
A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of…
Multiplicity-Free Gonality on Graphs
Frances Dean, Max Everett, Ralph Morrison
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 consi…