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It follows from the resolved Edge-statistics conjecture that if $H \\not \\in \\{K_k, \\bar K_k\\}$, then $\\mathrm{ind}(H) \\leq 1 / e + o_k(1)$. Equality holds for the star graph $K_{1, k-1}$, the graph with a single edge on $k$ vertices and their complements. 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