The Ramsey number of a long even cycle versus a star


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

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