  A 3-tournament is a complete 3-uniform hypergraph where each edge has a
special vertex designated as its tail. A vertex set $X$ dominates $T$ if every
vertex not in $X$ is contained in an edge whose tail is in $X$. The domination
number of $T$ is the minimum size of such an $X$. Generalizing well-known
results about usual (graph) tournaments, Gy\'arf\'as conjectured that there are
3-tournaments with arbitrarily large domination number, and that this is not
the case if any four vertices induce two triples with the same tail. In this
short note we solve both problems, proving the first conjecture and refuting
the second.
