An exponential improvement for diagonal Ramsey
| Autor: | Campos, Marcelo, Griffiths, Simon, Morris, Robert, Sahasrabudhe, Julian |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Ramsey number $R(k)$ is the minimum $n \in \mathbb{N}$ such that every red-blue colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove that \[ R(k) \leqslant (4 - \varepsilon)^k \] for some constant $\varepsilon > 0$. This is the first exponential improvement over the upper bound of Erd\H{o}s and Szekeres, proved in 1935. Comment: 57 pages, 8 figures |
| Databáze: | arXiv |
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