The generalized Ramsey number $f(n, 5, 8) = \frac 67 n + o(n)$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911062675161088 |
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| author | Bennett, Patrick Cushman, Ryan Dudek, Andrzej |
| author_facet | Bennett, Patrick Cushman, Ryan Dudek, Andrzej |
| contents | A $(p, q)$-coloring of $K_n$ is a coloring of the edges of $K_n$ such that every $p$-clique has at least $q$ distinct colors among its edges. The generalized Ramsey number $f(n, p, q)$ is the minimum number of colors such that $K_n$ has a $(p, q)$-coloring. Gomez-Leos, Heath, Parker, Schweider and Zerbib recently proved $f(n, 5, 8) \ge \frac 67 (n-1)$. Here we prove an asymptotically matching upper bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generalized Ramsey number $f(n, 5, 8) = \frac 67 n + o(n)$ Bennett, Patrick Cushman, Ryan Dudek, Andrzej Combinatorics A $(p, q)$-coloring of $K_n$ is a coloring of the edges of $K_n$ such that every $p$-clique has at least $q$ distinct colors among its edges. The generalized Ramsey number $f(n, p, q)$ is the minimum number of colors such that $K_n$ has a $(p, q)$-coloring. Gomez-Leos, Heath, Parker, Schweider and Zerbib recently proved $f(n, 5, 8) \ge \frac 67 (n-1)$. Here we prove an asymptotically matching upper bound. |
| title | The generalized Ramsey number $f(n, 5, 8) = \frac 67 n + o(n)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.01535 |