Modified anti-Ramsey formula conjecture for vertex-disjoint triangles

Let $n$ and $k$ be integers with $n\geq 3k$, let $kC_3$ be the vertex-disjoint union of $k$ triangles, and let $G_1(n,k),\ldots,G_4(n,k)$ be the four explicitly defined edge-colored graphs from the paper, with $c(G)$ denoting the number of colors used by $G$. Modified anti-Ramsey conjecture. There exists $n_0$ such that for every $n>n_0$ and every $k$ satisfying $n\geq 3k$,

$$ar(n,kC_3)=\max_{j\in[4]}c(G_j(n,k)).$$

This conjecture is motivated by extremal constructions for vertex-disjoint triangles and is proposed after the earlier Wu–Zhang–Li–Xie formula is disproved; the source provides no resolution.