Aharoni–Briggs–Kim–Kim conjecture for cycles

Let $C_t$ be a cycle with $t$ vertices, and let $f_{C_t}(n,n)$ denote the minimum number of independent $n$-sets in $C_t$ whose collection has a rainbow independent $n$-set. Aharoni–Briggs–Kim–Kim conjecture. If $t\ge 2n+1$, then

$$f_{C_t}(n,n)=n.$$

This is the cycle case of the lower-bound conjecture for rainbow independent sets. The source states that Lv and Lu confirmed the assertion when $t=2n+1$, while the full range $t\ge 2n+1$ is not resolved there.