Logo
All Random Solved Random Open
OPEN
Determine \[R(C_4,S_n),\] 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It was shown in [BEFRS89] that \[n+\lceil\sqrt{n}\rceil+1\geq R(C_4,S_n)\geq n+\sqrt{n}-6n^{11/40}.\] Füredi (unpublished) has shown that $R(C_4,S_n)=n+\lceil\sqrt{n}\rceil$ for infinitely many $n$.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.