A lower bound on the Ramsey number $R_k(k+1,k+1)$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Pudlák, Pavel Rödl, Vojtěch Wesley, William J. |
| author_facet | Pudlák, Pavel Rödl, Vojtěch Wesley, William J. |
| contents | We will prove that $R_k(k+1,k+1)\geq 4 tw_{\lfloor k/4\rfloor -3}(2)$, where $tw$ is the tower function defined by ${tw}_1(x)=x$ and ${tw}_{i+1}(x)=2^{{tw}_i(x)}$. We also give proofs of $R_k(k+1,k+2)\geq 4 tw_{k-7}(2)$, $R_k(k+1,2k+1)\geq 4 tw_{k-3}(2)$, and $R_k(k+2,k+2)\geq 4 tw_{k-4}(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A lower bound on the Ramsey number $R_k(k+1,k+1)$ Pudlák, Pavel Rödl, Vojtěch Wesley, William J. Combinatorics 05D10 We will prove that $R_k(k+1,k+1)\geq 4 tw_{\lfloor k/4\rfloor -3}(2)$, where $tw$ is the tower function defined by ${tw}_1(x)=x$ and ${tw}_{i+1}(x)=2^{{tw}_i(x)}$. We also give proofs of $R_k(k+1,k+2)\geq 4 tw_{k-7}(2)$, $R_k(k+1,2k+1)\geq 4 tw_{k-3}(2)$, and $R_k(k+2,k+2)\geq 4 tw_{k-4}(2)$. |
| title | A lower bound on the Ramsey number $R_k(k+1,k+1)$ |
| topic | Combinatorics 05D10 |
| url | https://arxiv.org/abs/2412.16637 |