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Determine \[R(C_4,S_n),\] where $S_n$ is the star on $n+1$ vertices.
#552
:
[BEFRS89]
graph theory
,
ramsey theory
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that \[n+\lceil\sqrt{n}\rceil+1\geq R(C_4,S_n)\geq n+\sqrt{n}-6n^{11/40}.\] Füredi (unpublished) has shown that $R(C_4,S_n)=n+\lceil\sqrt{n}\rceil$ for infinitely many $n$.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
.
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