Diagonal Ramsey numbers for wheels
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918516276330496 |
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| author | Li, Maoxuan Kashima, Masaki Mao, Yaping |
| author_facet | Li, Maoxuan Kashima, Masaki Mao, Yaping |
| contents | The Ramsey number $\mathrm{R}(G_1,G_2)$ is the smallest integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ contains either a red copy of $G_1$ or a blue copy of $G_2$. In 2022, the third author and others gave lower and upper bounds of the Ramsey number $\mathrm{R}(W_n,W_n)$, where $W_n$ is the wheel graph with $n$ vertices. In this paper, we improve their bounds by showing that $3n-2\leq \mathrm{R}(W_n,W_n)\leq 6n-6$ for even $n\geq 8$ and $2n\leq \mathrm{R}(W_n,W_n)\leq \frac{9n-7}{2}$ for odd $n\geq 7$. Furthermore, we give recursive bounds for the $k$-colored Ramsey number for $W_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagonal Ramsey numbers for wheels Li, Maoxuan Kashima, Masaki Mao, Yaping Combinatorics The Ramsey number $\mathrm{R}(G_1,G_2)$ is the smallest integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ contains either a red copy of $G_1$ or a blue copy of $G_2$. In 2022, the third author and others gave lower and upper bounds of the Ramsey number $\mathrm{R}(W_n,W_n)$, where $W_n$ is the wheel graph with $n$ vertices. In this paper, we improve their bounds by showing that $3n-2\leq \mathrm{R}(W_n,W_n)\leq 6n-6$ for even $n\geq 8$ and $2n\leq \mathrm{R}(W_n,W_n)\leq \frac{9n-7}{2}$ for odd $n\geq 7$. Furthermore, we give recursive bounds for the $k$-colored Ramsey number for $W_n$. |
| title | Diagonal Ramsey numbers for wheels |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.22116 |