Claims

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1983_03_01_erdos_hajnal_sos_szemeredi: Theorem 1 of Erdős, Hajnal, Sós and Szemerédi (Combinatorica 1983) with the arboricity-two membership of K_{2,2,2} gives every K_{2,2,2}-free graph with more than n^2/8 edges a linear independent set, the case delta > 1/8; refereed.

2026_10_03_jordan: A Lean construction of K_{2,2,2}-free graphs with edge density 3/2048 and sublinear independence number, credited by Conjectures.io to the solver Jordan and certified by that site on 6 October 2026; accepted on its review.

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