J. Richard Lundgren

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The competition graph of a loopless symmetric digraph If is the rwo-.\rc'p grclph. S,(H). Necessary and sufficient conditions on If are given for S,(ff) to be interval or unit interval. These are useful properties when application requires that the competition graph be efficiently colorable. Computational aspects are discussed. as are related open problems.(More)
Vertices x and y dominate a tournament T if for all vertices z 6 = x; y; either x beats z or y beats z. Let dom(T) be the graph on the vertices of T with edges between pairs of vertices that dominate T. We show dom(T) is either an odd cycle with possible pendant vertices or a forest of caterpillars. Since dom(T) is the complement of the competition graph of(More)
We study the minimum number of complete bipartite subgraphs needed to cover and partition the edges of a k-regular bigraph on 2n vertices. Bounds are determined on the minima of these numbers for fixed n and k. Exact values of the minima are found for all n and k 6 4. The same results hold for directed graphs. Equivalently, we have determined bounds on the(More)
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 (_q u) and (_Y, u) in D. We study competition graphs of acyclic digraphs D when the indegrees and outdegrees of the vertices of D are restricted. Under degree restrictions, we characterize the(More)
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(More)