  The traditional game of cops and robbers is played on undirected graph.
Recently, the same game played on directed graph is getting attention by more
and more people. We knew that if we forbid some subgraph we can bound the cop
number of the corresponding class of graphs. In this paper, we analyze the game
of cops and robbers on $\Vec{H}$-free digraphs. However, it is not the same as
the case of undirected graph. So we give a new concept ($\Vec{H}^*$-free) to
get a similar conclusion about the case of undirected graph.
