Chip-firing on the Platonic solids: a primer for studying graph gonality
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914860031279104 |
|---|---|
| author | Beougher, Marchelle Ding, Kexin Everett, Max Huang, Robin Lee, Chan Morrison, Ralph Weber, Ben |
| author_facet | Beougher, Marchelle Ding, Kexin Everett, Max Huang, Robin Lee, Chan Morrison, Ralph Weber, Ben |
| contents | 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~$9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chip-firing on the Platonic solids: a primer for studying graph gonality Beougher, Marchelle Ding, Kexin Everett, Max Huang, Robin Lee, Chan Morrison, Ralph Weber, Ben Algebraic Geometry Combinatorics 14T99, 05C57 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~$9$. |
| title | Chip-firing on the Platonic solids: a primer for studying graph gonality |
| topic | Algebraic Geometry Combinatorics 14T99, 05C57 |
| url | https://arxiv.org/abs/2407.05158 |