Duchêne–Kheddouci–Nowakowski–Tahraoui labeled packing conjecture for cycles

Let $C_n$ be a cycle of order $n=2k+x$, with $k\geq2$ and $1\leq x\leq2k-1$. The parameter $\lambda^k(C_n)$ is the largest number of labels in a labeling of the vertices that admits a packing of $k$ copies of $C_n$, with corresponding vertices receiving the same label. Labeled packing conjecture for cycles.

$$\lambda^k(C_n)= \begin{cases} 2,&\text{if }x=1\text{ and }k\text{ is even},\\ x+2,&\text{otherwise.} \end{cases}$$

This conjecture concerns the remaining values of the labeled packing number for cycles after the results cited in the paper. The supplied context gives no resolution status.