Craig W. Rasmussen

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For a nontrivial connected graph G, let c : V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6= NC(v) for every pair u, v of adjacent vertices of G. The minimum number of(More)
Based on our experience of 97 cases of chronic esophagitis diagnosed endoscopically and histologically by guided biopsies, a new macroscopial classification is suggested as follows: Type I: Erosive-ulcerative form; Type II: Granulative form;; Type III: Barrett-type ulcers; Type IV: Esophagogastric or marginal ulcerations; Type V: Stenosing form. Type I(More)
In our experience with five cases of Crohn's disease of the esophagus, the endoscopic appearance has been demonstrated. Corresponding to the basic pathological changes, the findings are very different, but two stages may be differentiated: Stage I in which inflammatory changes predominate as a mild or more often erosive-ulcerative esophagitis. Stage II is a(More)
In this paper we answer the following question: given a loopless symmetric digraph D with underlying interval graph H. what conditions are necessary and sufficient for the competition graph of D to be interval or unit interval‘? This question, first posed by Raychaudhuri and Roberts [lo]. was left open in our previous paper 171. In that paper we presented(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)
Large complex systems need to be analysed prior to operation so that those depending upon them for the protection of their information have a well defined understanding of the measures that have been taken to achieve security and the residual risk the system owner assumes during its operation. The U.S. military calls this analysis and vetting process(More)
Dedicated by the other authors to Professor John Maybee on the occasion of his 65th birthday. Abstract. One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in the work of Cohen 5, 6] on food webs. In this paper we consider this problem for the class of loopless(More)
The p-competition graph G of a digraph D is a graph on the same vertex set as D, with x; y] 2 E(G) if and only if jOut(x) \Out(y)j p in D. In this paper we focus on the case in which D is a symmetric digraph ((a; b) is an arc in D if and only if (b; a) is an arc in D). We relate the problem to 2-step graphs, squares, and a generalization of the neighborhood(More)
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