Drawing Series-Parallel Graphs on Restricted Integer 3D Grids
Di Giacomo, Emilio (2004) Drawing Series-Parallel Graphs on Restricted Integer 3D Grids. In: Graph Drawing 11th International Symposium, GD 2003, September 21-24, 2003, Perugia, Italy , pp. 238-246 (Official URL: http://dx.doi.org/10.1007/978-3-540-24595-7_22).
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A k-track drawing is a crossing-free 3D straight-line grid drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing is called the track number of G. In the existing literature a lower bound of five and an upper bound of fifteen are known for the track number of series-parallel graph. In this paper we reduce this gap for a large subclass of series-parallel graph for which the lower bound remains five but we show an upper bound of eight. We also describe a linear time drawing algorithm that computes a 3D straight-line grid drawing of these graphs in volume 4 × 4 × 2n.
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