Claims

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1997_12_01_erdos_gyarfas: Theorem 3 of Erdős and Gyárfás proves f(n) >= 5(n-1)/6 for n >= 4, f(n) <= n for odd n and f(n) <= n-1 for infinitely many even n: the lower half of f(n) ~ 5n/6, refereed in Combinatorica and credited by the site's curator.

2022_07_06_bennett_cushman_dudek_pralat: Theorem 1 of Bennett, Cushman, Dudek and Prałat proves f(n) = (5/6)n + o(n) for the least number of colors under which every K_4 of K_n spans at least five colors, by a randomized triangle-removal coloring process.

2022_08_26_joos_mubayi: Equation (2) of Joos and Mubayi proves r(K_n, K_4, 5) = 5n/6 + o(n), a second proof of the asymptotic of f(n) by a conflict-free hypergraph matching rather than a random process.

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