A new upper bound on the minimum degree of minimal Ramsey graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914865419911168 |
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| author | Bishnoi, Anurag Lesgourgues, Thomas |
| author_facet | Bishnoi, Anurag Lesgourgues, Thomas |
| contents | We prove that $s_r(K_{k+1}) = O(k^3 r^3 \log^3 k)$, where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05147 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new upper bound on the minimum degree of minimal Ramsey graphs Bishnoi, Anurag Lesgourgues, Thomas Combinatorics 05D10 (Primary) 51E12 (Secondary) We prove that $s_r(K_{k+1}) = O(k^3 r^3 \log^3 k)$, where $s_r(K_k)$ is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum degree of a graph $G$ such that any $r$-colouring of the edges of $G$ contains a monochromatic $K_k$, whereas no proper subgraph of $G$ has this property. |
| title | A new upper bound on the minimum degree of minimal Ramsey graphs |
| topic | Combinatorics 05D10 (Primary) 51E12 (Secondary) |
| url | https://arxiv.org/abs/2209.05147 |