P-COMPETITION GRAPHS

If D = (V, A) is a digraph, its p-competition graph has vertex set V and an edge between x and y if and only if there are distinct vertices a(1), ..., a(p) and arcs (x, a(i)) and (y, a(i)) in D for each i less than or equal to p. This definition generalities the widely studied p = 1 case of ordinary competition graphs. We obtain results about p-competition graphs analogous to the well-known results about ordinary competition graphs and apply these results to specific cases.