New bounds on the generalized Ramsey number $f(n,5,8)$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914720578011136 |
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| author | Gomez-Leos, Enrique Heath, Emily Parker, Alex Schwieder, Coy Zerbib, Shira |
| author_facet | Gomez-Leos, Enrique Heath, Emily Parker, Alex Schwieder, Coy Zerbib, Shira |
| contents | Let $f(n,p,q)$ denote the minimum number of colors needed to color the edges of $K_n$ so that every copy of $K_p$ receives at least $q$ distinct colors. In this note, we show $\frac{6}{7}(n-1) \leq f(n,5,8) \leq n + o(n)$. The upper bound is proven using the "conflict-free hypergraph matchings method" which was recently used by Mubayi and Joos to prove $f(n,4,5) = \frac{5}{6}n + o(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16365 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New bounds on the generalized Ramsey number $f(n,5,8)$ Gomez-Leos, Enrique Heath, Emily Parker, Alex Schwieder, Coy Zerbib, Shira Combinatorics Let $f(n,p,q)$ denote the minimum number of colors needed to color the edges of $K_n$ so that every copy of $K_p$ receives at least $q$ distinct colors. In this note, we show $\frac{6}{7}(n-1) \leq f(n,5,8) \leq n + o(n)$. The upper bound is proven using the "conflict-free hypergraph matchings method" which was recently used by Mubayi and Joos to prove $f(n,4,5) = \frac{5}{6}n + o(n)$. |
| title | New bounds on the generalized Ramsey number $f(n,5,8)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2308.16365 |