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Recall that a graph is triangle-free if it does not contain a copy of $K_3$. Also, for a graph $G$, $\alpha(G)$ shall denote its independence number. Lastly, we will write $o(1)$ to denote quantities ...

It is well known that the minimum number of monochromatic triangles in a red/blue coloring of the edges of the complete graph $K_n$ is given by Goodman's formula $$M(n)=\binom n3-\left\lfloor\frac n2\...