In general, determine the largest integer $f(r)$ such that every $r$-uniform hypergraph with chromatic number $3$ has a vertex contained in at least $f(r)$ many edges. It is easy to see that $f(2)=2$ and $f(3)=3$. Erdős did not know the value of $f(4)$.

This was solved by Erdős and Lovász [ErLo75], who proved in particular that there is a vertex contained in at least\[\frac{2^{r-1}}{4r}\]many edges.

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