Complementary cycle-factor conjecture for fully regular multipartite tournaments

Let $D$ be a $k$-fully regular $c$-partite tournament with $c\geq5$, meaning that for every pair of distinct partite sets, their induced bipartite tournament is $k$-regular. A $(p,|V(D)|-p)$-cycle-factor is a cycle-factor consisting of cycles of lengths $p$ and $|V(D)|-p$. Fully regular complementary cycle-factor conjecture. For every even $p$ satisfying

$$4\leq p\leq |V(D)|-4,$$

$D$ has a $(p,|V(D)|-p)$-cycle-factor. This is presented as an extension of the paper's results and as a weaker form of Yeo's conjecture; no resolution is supplied.