If D is an acyclic digraph, its competition graph has the same vertex set as D and an edge between vertices x and y if and only if for some vertex u, there are arcs (x,u) and (y,u) in D. The authors study competition graphs of acyclic digraphs D when the indegrees and outdegrees of the vertices of D are restricted. Under degree restrictions, they characterize the competition graphs and are able to solve the important open problem of characterizing acyclic digraphs whose competition graphs are interval graphs. The authors also characterize the competition graphs which are interval graphs.
