Revisiting Cases 2 and 11 of the Map Color Theorem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910141111074816 |
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| author | Sun, Timothy |
| author_facet | Sun, Timothy |
| contents | In 1968, Ringel and Youngs solved the remaining cases of the orientable Map Color Theorem by finding genus embeddings of the complete graphs $K_n$, for sufficiently large $n \equiv 2, 8, 11 \pmod{12}$. Following the approach previously explored by the author for $n \equiv 8 \pmod{12}$, we aim to streamline their constructions for $n \equiv 2, 11 \pmod{12}$ by finding families of current graphs with simpler patterns for the arc labelings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Cases 2 and 11 of the Map Color Theorem Sun, Timothy Combinatorics In 1968, Ringel and Youngs solved the remaining cases of the orientable Map Color Theorem by finding genus embeddings of the complete graphs $K_n$, for sufficiently large $n \equiv 2, 8, 11 \pmod{12}$. Following the approach previously explored by the author for $n \equiv 8 \pmod{12}$, we aim to streamline their constructions for $n \equiv 2, 11 \pmod{12}$ by finding families of current graphs with simpler patterns for the arc labelings. |
| title | Revisiting Cases 2 and 11 of the Map Color Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.06407 |