New bounds for Ramsey numbers involving graphs with a center
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910131543867392 |
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| author | Zhang, Yanbo Chen, Yaojun |
| author_facet | Zhang, Yanbo Chen, Yaojun |
| contents | Let $F_n$, $W_n$, and $\widehat{K}_n$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n-1$, respectively. In this paper, we give new bounds for the Ramsey numbers $R(F_n,F_m)$ and $R(W_n,W_n)$, which improve those due to Chen, Yu, and Zhao [EJC, 2021] and Mao, Wang, Magnant, and Schiermeyer [G&C, 2022], respectively, and establish lower and upper bounds for $R(\widehat{K}_n,\widehat{K}_n)$. Moreover, we present a blow-up technique to establish some new lower bounds for the Ramsey numbers of wheels versus cliques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New bounds for Ramsey numbers involving graphs with a center Zhang, Yanbo Chen, Yaojun Combinatorics Let $F_n$, $W_n$, and $\widehat{K}_n$ be the graphs obtained by joining a vertex to $n$ independent edges, a cycle and a path of order $n-1$, respectively. In this paper, we give new bounds for the Ramsey numbers $R(F_n,F_m)$ and $R(W_n,W_n)$, which improve those due to Chen, Yu, and Zhao [EJC, 2021] and Mao, Wang, Magnant, and Schiermeyer [G&C, 2022], respectively, and establish lower and upper bounds for $R(\widehat{K}_n,\widehat{K}_n)$. Moreover, we present a blow-up technique to establish some new lower bounds for the Ramsey numbers of wheels versus cliques. |
| title | New bounds for Ramsey numbers involving graphs with a center |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.13850 |