The Ramsey number of a long even cycle versus a star

Abstract

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