Claims

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1974_04_01_bondy_simonovits: Bondy and Simonovits (J. Combin. Theory Ser. B 1974) prove that more than 100k n^{1+1/k} edges force every even cycle C_{2l} with k <= l <= kn^{1/k}; with k = 3 this bounds ex(n,C_6) by 300 n^{4/3}, so c_3 = 1/6; refereed.

2018_07_13_conlon_lee: Theorem 5.1 of Conlon and Lee (Int. Math. Res. Not. IMRN 2021) bounds the extremal number of the one-subdivision of K_k by C_k n^{3/2 - 6^{-k}} for every k at least three, answering Problem 1021 with c_k = 6^{-k}.

2018_09_03_janzer: Theorem 3 of Janzer (Electron. J. Combin. 2019) bounds the extremal number of the one-subdivision of K_k by C_k n^{3/2 - 1/(4k-6)} for every k at least three, the sharpest exponent recorded for Problem 1021.

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