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For a fixed ρ ∈ 0, 1, what is (asymptotically) the minimal possible density g 3 (ρ) of triangles in a graph with edge density ρ? We completely solve this problem by proving that where t 1/ (1-) is the integer such that 1- 1t, 1- 1t+1.
Alexander Razborov (Fri,) studied this question.