The many-colour minimum colour-class conjecture for non-monochromatic triangles

Let $G=(V,E)$ be a $k$-edge-coloured graph with colouring

$$E=\bigsqcup_{i=1}^k E_i.$$

Many-colour minimum colour-class conjecture. If

$$|E_i|>\frac{1}{4k-2}|V|^2$$

for every $1\leq i\leq k$, then $G$ contains a non-monochromatic triangle.

This is presented as another many-colour variation of the paper's results on non-monochromatic triangles. The supplied text gives no evidence that the conjecture has been resolved.