The Ramsey number of a long even cycle versus a star

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