Claims

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1991_05_01_furedi: Füredi's 1991 theorem bounds the largest no-three-collinear subset guaranteed in n points with no four collinear: above c sqrt(n log n) and below o(n), refuting Erdős's expectation that g(n) >> n; refereed.

2017_04_17_balogh_solymosi: Balogh and Solymosi's Theorem 2.1 constructs n-point planar sets with no four collinear in which every subset of n^{5/6+o(1)} points has a collinear triple, so g(n) <= n^{5/6+o(1)}; refereed in Discrete Analysis.

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