J. Richard Lundgren

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With the increased sophistication of both computers and optimization software, linear programming problems of a size inconceivable to solve only a few years ago are now readily accessible. As model size and complexity increase, the issue of feasibility becomes a major issue in model development. This thesis explores the analysis of linear programming(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)
A tournament T is arc-traceable when each arc of the tournament is a part of a hamiltonian path. We characterize arc-traceable upset tournaments and show that this property is independent of the number of hamiltonian paths in such tournaments. We show that non-arc-traceable tournaments have a specific structure, and give several sufficient conditions for(More)
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)
The domination graph of a digraph has the same vertices as the digraph with an edge between two vertices if every other vertex loses to at least one of the two. Previously, the authors showed that the domination graph of a tournament is either an odd cycle with or without isolated and/or pendant vertices, or a forest of caterpillars. They also showed that(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)