OPEN
Determine the Ramsey number
\[R(C_4,S_n),\]
where $S_n$ is the star on $n+1$ vertices.
It was shown in
[BEFRS89] that
\[n+\lceil\sqrt{n}\rceil+1\geq R(C_4,S_n)\geq n+\sqrt{n}-6n^{11/40}.\]
Füredi (unpublished) has shown that $R(C_4,S_n)=n+\lceil\sqrt{n}\rceil$ for infinitely many $n$.
See also the entry in the graphs problem collection.
