We find the exact value of the Ramsey number $R(C_{2\ell },K_{1,n})$, when ℓ and $n=O({\ell }^{10/9})$ are large. Our result is closely related to the behaviour of Turán number $\mathrm{ex}(N,C_{2\ell })$ for an even cycle whose length grows quickly with N.

中文翻译：

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长偶数循环与恒星的拉姆齐数

我们找到拉姆齐数的确切值$R(C_{\mathrm{2个}\ell },{钾}_{\mathrm{1个},n})$, 当ℓ和$n=欧({\ell }^{10/9})$很大。我们的结果与图兰数的行为密切相关$\mathrm{前任}(否,C_{\mathrm{2个}\ell })$对于长度随N快速增长的偶数循环。