Symmetric Perfect $2$-colorings on $J(10,3)$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909129455435776 |
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| author | Tricot, Paul |
| author_facet | Tricot, Paul |
| contents | We study perfect $2$-coloring of the Johnson graphs $J(n,3)$ associated with the third largest eigenvalue and symmetric quotient matrix, which exists only when $n \in \{6, 10\}$. We survey the known constructions in the case $n=6$, give a new construction for the two known perfect $2$-colorings in the case $n=10$, and prove that these are the only possible ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric Perfect $2$-colorings on $J(10,3)$ Tricot, Paul Combinatorics We study perfect $2$-coloring of the Johnson graphs $J(n,3)$ associated with the third largest eigenvalue and symmetric quotient matrix, which exists only when $n \in \{6, 10\}$. We survey the known constructions in the case $n=6$, give a new construction for the two known perfect $2$-colorings in the case $n=10$, and prove that these are the only possible ones. |
| title | Symmetric Perfect $2$-colorings on $J(10,3)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.03474 |