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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.14568 |
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| _version_ | 1866914698597761024 |
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| author | Tikhomirov, Konstantin |
| author_facet | Tikhomirov, Konstantin |
| contents | A well known conjecture of Burr and Erdos asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that $r(Q_n)=O(2^{2n-c n})$ for a universal constant $c>0$, improving upon the previous best known bound $r(Q_n)=O(2^{2n})$, due to Conlon, Fox and Sudakov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14568 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A remark on the Ramsey number of the hypercube Tikhomirov, Konstantin Combinatorics A well known conjecture of Burr and Erdos asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that $r(Q_n)=O(2^{2n-c n})$ for a universal constant $c>0$, improving upon the previous best known bound $r(Q_n)=O(2^{2n})$, due to Conlon, Fox and Sudakov. |
| title | A remark on the Ramsey number of the hypercube |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2208.14568 |