Solution on strong partition of $2$-balanced regular multipartite tournaments

We call a partition of a c-partite tournament into tournaments of order c is strong if each tournament is strongly connected. The strong partition number denoted as $ST(r)$, represents the minimum integer $c'$ such that every regular r-balanced c-partite tournament has a strong partition with c≥ c'. Figueroa, Montellano-Ballesteros and Olsen showed the existence of $ST(r)$ for all r≥ 2 and proved that 5≤ ST(2)≤ 7. In this note, we establish that $ST(2)=6$ and we also show the unique $2$-balanced $5$-partite tournament which has no strong partition.