Authors

• Lisa Cenek University of Illinois Chicago, United States
• Lizzie Ferguson Williams College, United States
• Eyobel Gebre University of Pennsylvania, United States
• Cassandra Marcussen Harvard University, United States
• Jason Meintjes San Francisco State University, United States
• Ralph Morrison Williams College, United States https://orcid.org/0000-0001-7134-1521
• Liz Ostermeyer Williams College, United States
• Shefali Ramakrishna Cornell University, United States
• Ben Weber Williams College, United States

DOI: https://doi.org/10.26493/2590-9770.1792.fb4 Keywords: Graph theory, tree-cut decomposition, scramble number, gonality Abstract

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 a variation of the existing literature on tree-cut decompositions.  We prove that this invariant serves as an upper bound on scramble number, though they are not always equal.  We study properties of screewidth, and present results and conjectures on its connection to divisorial gonality.