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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.16905 |
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| _version_ | 1866909384697708544 |
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| author | Kurkofka, Jan Nevinson, Emily |
| author_facet | Kurkofka, Jan Nevinson, Emily |
| contents | We propose an open question that seeks to generalise the Four Colour Theorem from two to three dimensions. As an appetiser, we show that 12 instead of four colours are both sufficient and necessary to colour every 2-complex that embeds in a prescribed 3-manifold. However, our example of a 2-complex that requires 12 colours is not simplicial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the edge-chromatic number of 2-complexes Kurkofka, Jan Nevinson, Emily Combinatorics Geometric Topology 05C10, 05C15 We propose an open question that seeks to generalise the Four Colour Theorem from two to three dimensions. As an appetiser, we show that 12 instead of four colours are both sufficient and necessary to colour every 2-complex that embeds in a prescribed 3-manifold. However, our example of a 2-complex that requires 12 colours is not simplicial. |
| title | On the edge-chromatic number of 2-complexes |
| topic | Combinatorics Geometric Topology 05C10, 05C15 |
| url | https://arxiv.org/abs/2310.16905 |