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arXiv · 2407.05158

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

Marchelle Beougher·Kexin Ding·Max Everett·Robin Huang·Chan Lee·Ralph Morrison·Ben Weber
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Abstract

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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Marchelle Beougher, Kexin Ding, Max Everett, Robin Huang, Chan Lee, Ralph Morrison, Ben Weber. 2024-07-06. Chip-firing on the Platonic solids: a primer for studying graph gonality. https://arxiv.org/abs/2407.05158

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