Cambie–de Verclos–Kang conjecture on triangles in regular graphs

For positive integers $n$ and $k$, let $t(n,k)$ be the minimum number of triangles over all $k$-regular graphs on $n$ vertices. Let $\mathcal{G}(n,k)$ denote the family of extremal graphs referred to in the source.

Cambie–de Verclos–Kang conjecture. For every odd integer $n$ and even integer $k$ with

$$\frac{2n}{5}< k< \frac{n}{2},$$ $$t(n,k)=\frac{k}{4}(3k-n-1).$$

Moreover, the extremal graphs must belong to $\mathcal{G}(n,k)$.

This conjecture seeks the exact minimum number of triangles in regular graphs in the range above, together with a characterization of all extremal graphs. The paper records it as a conjecture of Cambie, de Joannis de Verclos, and Kang; the supplied material gives no resolution.