Four-coloring Eulerian triangulations of the torus
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929519641755648 |
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| author | Brianski, Marcin Kral, Daniel Lamaison, Ander Shu, Xichao |
| author_facet | Brianski, Marcin Kral, Daniel Lamaison, Ander Shu, Xichao |
| contents | Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high representativity is 4-colorable. We give an explicit bound on the representativity in the case of the torus by proving that every Eulerian triangulation of the torus with representativity at least 10 is 4-colorable. We also observe that the bound on the representativity cannot be decreased to less than 8 as there exists a non-4-colorable Eulerian triangulation of the torus with representativity 7. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Four-coloring Eulerian triangulations of the torus Brianski, Marcin Kral, Daniel Lamaison, Ander Shu, Xichao Combinatorics Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high representativity is 4-colorable. We give an explicit bound on the representativity in the case of the torus by proving that every Eulerian triangulation of the torus with representativity at least 10 is 4-colorable. We also observe that the bound on the representativity cannot be decreased to less than 8 as there exists a non-4-colorable Eulerian triangulation of the torus with representativity 7. |
| title | Four-coloring Eulerian triangulations of the torus |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.19165 |