Ramsey numbers of sparse graphs versus disjoint books
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908448717799424 |
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| author | Huang, Ting Zhang, Yanbo Chen, Yaojun |
| author_facet | Huang, Ting Zhang, Yanbo Chen, Yaojun |
| contents | Let $B_k$ denote a book on $k+2$ vertices and $tB_k$ be $t$ vertex-disjoint $B_k$'s. Let $G$ be a connected graph with $n$ vertices and at most $n(1+ε)$ edges, where $ε$ is a constant depending on $k$ and $t$. In this paper, we show that the Ramsey number $$r(G,tB_k)=2n+t-2$$ provided $n\ge 111t^3k^3$. Our result extends the work of Erdős, Faudree, Rousseau, and Schelp (1988), who established the corresponding result for $G$ being a tree and $t=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey numbers of sparse graphs versus disjoint books Huang, Ting Zhang, Yanbo Chen, Yaojun Combinatorics 05C55, 05D10 Let $B_k$ denote a book on $k+2$ vertices and $tB_k$ be $t$ vertex-disjoint $B_k$'s. Let $G$ be a connected graph with $n$ vertices and at most $n(1+ε)$ edges, where $ε$ is a constant depending on $k$ and $t$. In this paper, we show that the Ramsey number $$r(G,tB_k)=2n+t-2$$ provided $n\ge 111t^3k^3$. Our result extends the work of Erdős, Faudree, Rousseau, and Schelp (1988), who established the corresponding result for $G$ being a tree and $t=1$. |
| title | Ramsey numbers of sparse graphs versus disjoint books |
| topic | Combinatorics 05C55, 05D10 |
| url | https://arxiv.org/abs/2507.09827 |