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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.02593 |
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| _version_ | 1866911789198868480 |
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| author | Chng, Zhi Yee Britz, Thomas Tan, Ta Sheng Wong, Kok Bin |
| author_facet | Chng, Zhi Yee Britz, Thomas Tan, Ta Sheng Wong, Kok Bin |
| contents | The Ramsey numbers $R(T_n,W_8)$ are determined for each tree graph $T_n$ of order $n\geq 7$ and maximum degree $Δ(T_n)$ equal to either $n-4$ or $n-5$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that $R(T_n,W_m) = 2n-1$ for each tree graph $T_n$ of order $n\geq m-1$ with $Δ(T_n)\leq n-m+2$ when $m\geq 4$ is even. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ramsey numbers for trees of order $n$ with maximum degree at least $n-5$ versus the wheel graph of order nine Chng, Zhi Yee Britz, Thomas Tan, Ta Sheng Wong, Kok Bin Combinatorics 05C55, 05D10 The Ramsey numbers $R(T_n,W_8)$ are determined for each tree graph $T_n$ of order $n\geq 7$ and maximum degree $Δ(T_n)$ equal to either $n-4$ or $n-5$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that $R(T_n,W_m) = 2n-1$ for each tree graph $T_n$ of order $n\geq m-1$ with $Δ(T_n)\leq n-m+2$ when $m\geq 4$ is even. |
| title | The Ramsey numbers for trees of order $n$ with maximum degree at least $n-5$ versus the wheel graph of order nine |
| topic | Combinatorics 05C55, 05D10 |
| url | https://arxiv.org/abs/2403.02593 |