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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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
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Algorithms
Games
Icosahedrons
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creator Beougher, Marchelle
Ding, Kexin
Everett, Max
Huang, Robin
Chan, Lee
Morrison, Ralph
Weber, Ben
description 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~\(9\).
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subjects Algorithms
Games
Icosahedrons
title Chip-firing on the Platonic solids: a primer for studying graph gonality
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