Claims

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1970_01_01_toft: Toft's 1970 constructions give k-critical graphs with c_k n^2 edges for every k at least 4, answering the first question yes, and beat the proposed formula for k at least 6 not a multiple of 3; refereed in Studia Sci. Math. Hungar.

2026_09_05_gu: Qiyuan Gu's AI-assisted September 2026 preprint claims 12-critical graphs with (2/5 + o(1))n^2 edges, above the proposed 3n^2/8 at k = 12, refuting the asymptotic at a multiple of 3; unreviewed, not refereed.

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