Zhu et al.'s five-color conjecture for generalized Petersen graphs

Let $n$ and $k$ be integers with $n\geq 2k$, and let $GP(n,k)$ be the generalized Petersen graph with star chromatic index $\chi^\prime_s(GP(n,k))$, the smallest number of colors in a proper edge coloring in which no path or cycle with four edges is bicolored. Zhu et al.'s conjecture. If $GP(n,k)\neq GP(3,1)$, then

$$\chi^\prime_s(GP(n,k))\leq 5.$$

The conjecture asserts that $GP(3,1)$ is the unique generalized Petersen graph requiring more than five colors for a star edge coloring. The paper proves the assertion for the case $n\geq 2k$ and $\gcd(n,k)\geq 3$, but the general claim remains open based on the supplied text.