  Competition graphs were created in connected to a biological model as a means
of reflecting the competition relations among the predators in the food webs
and determining the smallest dimension of ecological phase space. In 2011,
Factor and Merz introduced the (1,2)-step competition graph of a digraph. Given
a digraph $D=(V,A)$, the (1,2)-step competition graph of $D$, denoted
$C_{1,2}(D)$, is a graph on $V(D)$ where $xy\in E(C_{1,2}(D))$ if and only if
there exists a vertex $z\neq x,y$ such that either $d_{D-y}(x,z)=1$ and
$d_{D-x}(y,z)\leq 2$ or $d_{D-x}(y,z)=1$ and $d_{D-y}(x,z)\leq 2$. They also
characterized the (1,2)-step competition graphs of tournaments and extended
some results to the $(i,j)$-step competition graphs of tournaments. In this
paper, the definition of the (1,2)-step competition graph of a digraph is
generalized to the one of a hypertournament and the $(1,2)$-step competition
graph of a $k$-hypertournament is characterized. Also, the results are extended
to the $(i,j)$-step competition graph of a $k$-hypertournament.
