Claims

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1995_05_15_alon_erdos: Alon and Erdős's 1996 Theorem 1.1, placing f(n) between n^{1/3}/(log n)^{4/3} and n^{1/3}(log log n)^{1/3}/(log n)^{1/3} up to constants, so that f(n) = n^{1/3+o(1)}; refereed, and recorded by the site.

2006_11_16_vu: Vu's 2007 improvement of the Alon–Erdős lower bound to f(n) at least a constant times n^{1/3}/log n; refereed, and recorded by the site; the paper is not held here.

2021_04_30_conlon_fox_pham: Theorem 1.5 of the 2021 preprint of Conlon, Fox and Pham, determining f(n) up to a constant factor as n^{1/3}(n/phi(n))/((log n)^{1/3}(log log n)^{2/3}); accepted by the site as the solution; to appear in J. Eur. Math. Soc.

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