Mao, Wang, Magnant, and Schiermeyer's Gallai-Ramsey conjecture for the fan $F_3$

A fan $F_n$ is the graph obtained by joining a new central vertex to every vertex of a matching of size $n$, and $GR_k(F_3)$ is its $k$-color Gallai-Ramsey number.

Mao, Wang, Magnant, and Schiermeyer's conjecture. For $k\ge2$,

$$GR_k(F_3)= \begin{cases} 14\cdot5^{(k-2)/2}-1, & \text{if } k \text{ is even};\\ 33\cdot5^{(k-3)/2}, & \text{if } k \text{ is odd}. \end{cases}$$

The paper supplies a new lower bound that exceeds the conjectured value for even $k$, so this conjecture is disproved.