Ramsey with purple edges
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915293036544000 |
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| author | Lesgourgues, Thomas Liebenau, Anita Taylor, Nye |
| author_facet | Lesgourgues, Thomas Liebenau, Anita Taylor, Nye |
| contents | Motivated by a question of Angell, we investigate a variant of Ramsey numbers where some edges are coloured simultaneously red and blue, which we call purple. Specifically, we are interested in the largest number $g=g(n;s,t)$, for some $s$ and $t$ and $n<R(s,t)$, such that there exists a red/blue/purple colouring of $K_n$ with $g$ purple edges, with no red/purple copy of $K_s$ nor blue/purple copy of $K_t$. We determine $g$ asymptotically for a large family of parameters, exhibiting strong dependencies with Ramsey-Turán numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_01034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey with purple edges Lesgourgues, Thomas Liebenau, Anita Taylor, Nye Combinatorics 05D10, 05D40, 05C35, 05C55 Motivated by a question of Angell, we investigate a variant of Ramsey numbers where some edges are coloured simultaneously red and blue, which we call purple. Specifically, we are interested in the largest number $g=g(n;s,t)$, for some $s$ and $t$ and $n<R(s,t)$, such that there exists a red/blue/purple colouring of $K_n$ with $g$ purple edges, with no red/purple copy of $K_s$ nor blue/purple copy of $K_t$. We determine $g$ asymptotically for a large family of parameters, exhibiting strong dependencies with Ramsey-Turán numbers. |
| title | Ramsey with purple edges |
| topic | Combinatorics 05D10, 05D40, 05C35, 05C55 |
| url | https://arxiv.org/abs/2505.01034 |