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Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (site viewed on Feb. 5, 2007). PDF text: 66 p. : ill. (some col.) UMI publication number: AAT 3216432. Includes bibliographical references. Also available in microfilm and microfiche format.

Thesis (Ph. D.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains vi, 52 p. : ill. Includes abstract. Includes bibliographical references (p. 50-52).

Given a finite set S of n nonintersecting line segments with no three end points collinear, the segment end point visibility graph is defined as the graph whose vertices are the end points of the line segments in S and two vertices are adjacent if the straight line segment joining two end points does not intersect any element of S, or if they are end points of the same segment. Segment end point visibility graphs have a wide variety of applications in VLSI circuit design, study of art gallery problems, and other areas of computational geometry. This thesis contains a survey of the important results that are currently known regarding the characterization of these graphs. Also a weak visibility dual of a segment end point visibility graph is defined and some structural properties of such graphs are presented. Some open problems and questions related to the characterization of weak visibility graphs are also discussed. / Department of Mathematical Sciences

Thesis (M.Sc.). / Written for the Dept. of Mathematics and Statistics. Title from title page of PDF (viewed 2008/05/29). Includes bibliographical references.

Thesis (M.Sc.). / Written for the Dept. of Mathematics and Statistics. Title from title page of PDF (viewed 2008/04/12). Includes bibliographical references.

Interval graphs admit elegant ordering and structural characterizations. A natural digraph analogue of interval graphs, called chronological interval digraphs, has recently been identified and studied. We introduce the class of chronological rectangle digraphs, and show that they are a higher dimensional analogue of chronological interval digraphs. A main goal of this thesis is to establish a foundation of knowledge about this class, including basic properties and an ordering characterization. Our most significant result is a forbidden induced subdigraph characterization for the series-parallel digraphs which are chronological rectangle. We also discuss obtaining chronological rectangle digraphs from orientations of graphs. In addition we introduce the related concept of the chronological interval dimension of a digraph, and determine the digraphs for which it is defined. Unit and proper chronological rectangle digraphs, defined analogously to unit and proper interval graphs, are also introduced and studied. / Graduate

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