A new view of hypercube genus
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913181504372736 |
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| author | Hammack, Richard H. Kainen, Paul C. |
| author_facet | Hammack, Richard H. Kainen, Paul C. |
| contents | Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the $n$-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube's 2-skeleton. For odd dimension $n$, the entire 2-skeleton decomposes into $(n-1)/2$ copies of the surface, and the intersection of any two copies is the hypercube graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00070 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new view of hypercube genus Hammack, Richard H. Kainen, Paul C. Combinatorics 05C10, 05C51, 57M15 Beineke, Harary and Ringel discovered a formula for the minimum genus of a torus in which the $n$-dimensional hypercube graph can be embedded. We give a new proof of the formula by building this surface as a union of certain faces in the hypercube's 2-skeleton. For odd dimension $n$, the entire 2-skeleton decomposes into $(n-1)/2$ copies of the surface, and the intersection of any two copies is the hypercube graph. |
| title | A new view of hypercube genus |
| topic | Combinatorics 05C10, 05C51, 57M15 |
| url | https://arxiv.org/abs/2401.00070 |