Claims

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1994_09_01_erdos_hajnal_simonovits_sos_szemeredi: The upper bound delta_3(5) at most 1/12 proves the statement for every delta above 1/12; refereed in Combin. Probab. Comput. 3 (1994).

2011_09_20_balogh_lenz: Theorem 3 of Balogh and Lenz gives theta_3(K_5) at least 1/64, so K_5-free graphs with sublinear triangle-free sets can have quadratically many edges; refereed in Israel J. Math. 194 (2013) and credited by the site.

2021_03_18_liu_reiher_sharifzadeh_staden: Theorem 1.1 and Corollary 1.2 of Liu, Reiher, Sharifzadeh and Staden give K_5-free graphs with sublinear triangle-free sets and (1/12 - o(1)) n^2 edges, so delta_3(5) = 1/12; refereed in J. Eur. Math. Soc. 28 (2025).

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