  The notion of p-competition graphs of digraphs was introduced by S-R. Kim, T.
A. McKee, F. R. McMorris, and F. S. Roberts [p-competition graphs, Linear
Algebra Appl., 217 (1995) 167--178] as a generalization of the competition
graphs of digraphs. Let p be a positive integer. The p-competition graph C_p(D)
of a digraph D=(V,A) is a (simple undirected) graph which has the same vertex
set V and has an edge between distinct vertices x and y if and only if there
exist p distinct vertices v_1, ..., v_p in V such that (x,v_i), (y,v_i) are
arcs of the digraph D for each i=1, ..., p.
  In this paper, given a cycle of length n, we compute exact values of p in
terms of n such that it is a p-competition graph, which generalizes the results
obtained by Kim et al. We also find values of p in terms of n so that its
complement is a p-competition graph.
