Petrovic's two 4-kings conjecture for bipartite hypertournaments

Let $B$ be a bipartite $k$-hypertournament, where $k\ge 2$. A vertex is a transmitter if it has no incoming arc with any vertex from a different partite set, and a 4-king is a vertex from which every vertex is reachable by a path of length at most $4$. Petrovic's conjecture. If $B$ has no transmitters, then each partite set of $B$ contains at least two 4-kings. The conjecture is motivated by the corresponding theorem for bipartite tournaments; its resolution is not stated in the supplied text.