Perfect colourings of simplices and hypercubes in dimension four and five with few colours
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914694712786944 |
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| author | Frettlöh, Dirk |
| author_facet | Frettlöh, Dirk |
| contents | A vertex colouring of some graph is called perfect if each vertex of colour $i$ has the same number $a_{ij}$ of neighbours of colour $j$. Here we determine all perfect colourings of the edge graphs of the hypercube in dimensions 4 and 5 by two and three colours, respectively. For comparison we list all perfect colourings of the edge graphs of the simplex in dimensions 4 and 5, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perfect colourings of simplices and hypercubes in dimension four and five with few colours Frettlöh, Dirk Combinatorics 05C15 A vertex colouring of some graph is called perfect if each vertex of colour $i$ has the same number $a_{ij}$ of neighbours of colour $j$. Here we determine all perfect colourings of the edge graphs of the hypercube in dimensions 4 and 5 by two and three colours, respectively. For comparison we list all perfect colourings of the edge graphs of the simplex in dimensions 4 and 5, respectively. |
| title | Perfect colourings of simplices and hypercubes in dimension four and five with few colours |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2402.18457 |