Orthogonal 3D Shapes of Theta Graphs
Di Giacomo, Emilio and Liotta, Giuseppe and Patrignani, Maurizio (2002) Orthogonal 3D Shapes of Theta Graphs. In: Graph Drawing 10th International Symposium, GD 2002, August 26-28, 2002, Irvine, CA, USA , pp. 142-149 (Official URL: http://dx.doi.org/10.1007/3-540-36151-0_14).
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The recent interest in three dimensional graph drawing has been motivating studies on how to extend two dimensional techniques to higher dimensions. A common approach for computing a 2D orthogonal drawing of a graph separates the task of defining the shape of the drawing from the task of computing its coordinates. First results towards finding a three-dimensional counterpart of this approach are presented in [8,9], where characterizations of orthogonal r epresentations of paths and cycles are studied. In this note we show that the known characterization for cycles does not immediately extend to even seemingly simple graphs such as theta graphs. A sufficient condition for recognizing three-dimensional orthogonal representations of theta graphs is also presented.
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