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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.01274 |
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| _version_ | 1866916214765256704 |
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| author | Dubó, Freddy Flores Stein, Maya |
| author_facet | Dubó, Freddy Flores Stein, Maya |
| contents | The double star $S(m_1,m_2)$ is obtained from joining the centres of a star with $m_1$ leaves and a star with $m_2$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S(m_1,m_2)$, for positive $m_1,m_2$ fulfilling $(\sqrt 5+1)m_2/2 < m_1 < 3m_2$. Our result implies that for all positive $m$, the Ramsey number of the double star $S(2m,m)$ is at most $4.275m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Ramsey number of the double star Dubó, Freddy Flores Stein, Maya Combinatorics The double star $S(m_1,m_2)$ is obtained from joining the centres of a star with $m_1$ leaves and a star with $m_2$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S(m_1,m_2)$, for positive $m_1,m_2$ fulfilling $(\sqrt 5+1)m_2/2 < m_1 < 3m_2$. Our result implies that for all positive $m$, the Ramsey number of the double star $S(2m,m)$ is at most $4.275m$. |
| title | On the Ramsey number of the double star |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.01274 |