Since the chromatic number is always equal or greater than the clique number, the chromatic number of the visibility graph of sets in A is also unbounded.
Cibulka, Kyncl and Valtr have also indirectly solved problem 2.
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Problem 2 solved
Since the chromatic number is always equal or greater than the clique number, the chromatic number of the visibility graph of sets in A is also unbounded.
Cibulka, Kyncl and Valtr have also indirectly solved problem 2.