The Gamma-Switch Ramsey Number
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914489146802176 |
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| author | Duffy, Christopher Fok, Benjamin MacGillivray, Gary |
| author_facet | Duffy, Christopher Fok, Benjamin MacGillivray, Gary |
| contents | We define and develop preliminary theoretical results for the $Γ$-switch Ramsey number, a variation on the classical $m$-colour Ramsey number for which we allow permuting the colours incident with a vertex using elements of a group $Γ\leq S_m$. We find bounds for the $Γ$-switch Ramsey number for groups with various properties as a function of the classical parameter. We prove $R_{C_3}(4,4,4) = R(3,3,3) + 1$, $R_{C_4}(3,4,3,4) = R(2,3,2,3) + 1$ and $43 \leq R_{C_4}(4,4,4,4) \leq R(3,3,3,3) + 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17684 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Gamma-Switch Ramsey Number Duffy, Christopher Fok, Benjamin MacGillivray, Gary Combinatorics 05D10 We define and develop preliminary theoretical results for the $Γ$-switch Ramsey number, a variation on the classical $m$-colour Ramsey number for which we allow permuting the colours incident with a vertex using elements of a group $Γ\leq S_m$. We find bounds for the $Γ$-switch Ramsey number for groups with various properties as a function of the classical parameter. We prove $R_{C_3}(4,4,4) = R(3,3,3) + 1$, $R_{C_4}(3,4,3,4) = R(2,3,2,3) + 1$ and $43 \leq R_{C_4}(4,4,4,4) \leq R(3,3,3,3) + 1$. |
| title | The Gamma-Switch Ramsey Number |
| topic | Combinatorics 05D10 |
| url | https://arxiv.org/abs/2604.17684 |