Čada–Kaneko–Ryjáček conjecture on minimum color degree and rainbow cycles

Let $G$ be an edge-colored graph with $n=|V(G)|$ vertices, and let $\delta^c(G)$ denote its minimum color degree. For an integer $k$, a rainbow cycle is a cycle whose edges have pairwise distinct colors.

Čada–Kaneko–Ryjáček conjecture. If

$$\delta^c(G)\geq \frac{n+k}{2},$$

then $G$ contains a rainbow-cycle subgraph of length at least $k$.

This conjecture generalizes the known sufficient condition that $\delta^c(G)>\frac{n}{2}+2$ guarantees a rainbow cycle of length at least four. The source does not provide evidence that the conjecture has been resolved.