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Competition graphs were rst introduced by Joel Cohen in the study of food webs and have since been extensively studied. Graphs which are the competition graph of a strongly connected or Hamiltonian digraph are of particular interest in applications to communication networks. It has been previously established that every graph without isolated vertices (except K 2) which is the competitiongraph of a loopless digraph is also the competitiongraph of a strongly connecteddigraph. We establish an analogous result for one generalization of competition graphs, the p-competition graph. Furthermore, we establish some large classes of graphs, including trees, as the p-competition graph of a loopless Hamiltonian digraph. and show that interval graphs on n 4 vertices are the 2-competition graphs of loopless Hamiltonian digraphs.

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