2 problems

For a digraph $D$, let $c(D)$ be the largest integer $k$ for which there are directed cycles $C_1,\ldots,C_k$ through a common vertex $v$ such that $C_1-v,\ldots,C_k-v$ are pairwis…

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…