The (1,2)-Step Competition Graph Of A Hypertournament

Y In 2011, Factor and Merz [Discrete Appl. Math. 159 (2011), 100-103] defined 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,C-2(D), is a graph on V(D), where xy is an element of E(C-1,C-2(D)) if and only if there exists a vertex z not equal x, y such that either d(D-y) (x, z) = 1 and d(D-x) (y, z) <= 2 or d(D-x) (y, z) = 1 and d(D-y) (x, z) <= 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 a hypertournament and the (1, 2)-step competition graph of a k-hypertournament is characterized. Also, the results are extended to (i, j)-step competition graphs of k-hypertournaments.