AlphaEvolve problems·alphaevolve:46
Minimal triangle density in graphs
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For $0 \\leq \\rho \\leq 1$, let $C(\\rho)$ denote the largest quantity such that any graph on $n$ vertices and $(\\rho+o(1)) \\binom{n}{2}$ edges will have at least $(C(\\rho)-o(1)) \\binom{n}{3}$ triangles. What is $C(\\rho)$?
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