On the Minimal Density of Triangles in Graphs

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-ρ) is the integer such that ρ∈[ 1- 1t,1- 1t+1] .