The cycle rainbow matching conjecture

Let $C_t$ be the cycle on $t$ vertices, and let $f_{C_t}(s,s)$ denote the least number of independent sets of size $s$ in $C_t$ that guarantees a rainbow independent set of size $s$. Cycle rainbow matching conjecture. If

$$s<\frac{t}{2},$$

then

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

The source presents this as a possible explanation for the jump between the almost-full and full rainbow matching problems.