Matching sequencibility conjecture for complete multi-partite graphs

Let $K_{s(n)}$ be the complete $s$-partite graph with each part of size $n$. For an ordering of the edges, let $ms$ denote matching sequencibility, and let $cms$ denote cyclic matching sequencibility.

Matching sequencibility conjecture. For any integers $n\geq 2$ and $s\geq 2$,

$$ms(K_{s(n)})=cms(K_{s(n)})=\left\lfloor\frac{sn}{2}\right\rfloor-1.$$

This conjecture proposes an exact common value for the ordinary and cyclic matching sequencibility of complete equipartite graphs. The supplied text does not indicate whether it has been proved or disproved.