On Intersection Graphs of Segments with Prescribed Slopes
Cerný, Jakub and Král, Daniel and Nyklová, Helena and Pangrác, Ondrej (2002) On Intersection Graphs of Segments with Prescribed Slopes. In: Graph Drawing 9th International Symposium, GD 2001, September 23-26, 2001, Vienna, Austria , pp. 261-271 (Official URL: http://dx.doi.org/10.1007/3-540-45848-4_21).
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We study intersection graphs of segments with prescribed slopes in the plane. A sufficient and necessary condition on tuples of slopes in order to define the same class of graphs is presented for both the possibilities that the parallel segments can or cannot overlap. Classes of intersection graphs of segments with four slopes are fully described; in particular, we find an infinite set of quadruples of slopes which define mutually distinct classes of intersection graphs of segments with those slopes.
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