Chip-firing on the Platonic solids: a primer for studying graph gonality

This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques for studying these games, including independent sets, treewidth, scramble number, and Dhar's burning algorithm. In...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Beougher, Marchelle, Ding, Kexin, Everett, Max, Huang, Robin, Chan, Lee, Morrison, Ralph, Weber, Ben
Format: Article
Language:English
Subjects:
Algorithms
Games
Icosahedrons
Online Access:Get full text
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Summary:This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques for studying these games, including independent sets, treewidth, scramble number, and Dhar's burning algorithm. In addition to showcasing some previously known results, we present the first proofs that the dodecahedron graph has gonality \(6\), and that the icosahedron graph has gonality~\(9\).
ISSN:2331-8422