Rainbow triangles in edge-colored graphs with large minimum color degree

Let $G$ be an edge-colored graph on $n$ vertices, and let $\text{deltac}(G)$ denote its minimum color degree. Li and, independently Li, Ning, Xu, and Zhang, proved that every edge-colored graph on $n$ vertices with $\text{deltac}(G)\ge \frac{n+1}{2}$ contains a rainbow triangle. Let $\text{rt}(G)$ denote the number of rainbow triangles in $G$, and define $$f(n)=\min \{\text{rt}(G):\mathrm{\mid }V(G)\mathrm{\mid }=n,\text{deltac}(G)\ge (n+1)\mathrm{/}2\}\mathrm{.}$$ In \cite{LiNingShiZhang2024}, the following open problem was posed: determine all the values of $f(n)$. In this paper, we determine $f(n)$ completely: $f(n)=(n^2-1)\mathrm{/}8$ for odd $n\ge 3$, $f(n)=\frac{n^2}{4}-1$ for all even $n\ge 6,$ and $f(4)=4$. This resolves an open problem raised in \cite{LiNingShiZhang2024}.