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3D Straight-line Drawings of k-trees

This paper studies the problem of computing 3D crossing-free straight-line grid drawings of graphs such that the overall volume is small. We show that every 2-tree (and therefore every series-parallel graph) can be drawn on an integer 3D grid consisting of 15 parallel lines and having linear volume. We extend the study to the problem of drawing general k-trees on a set of parallel grid lines. Lower bounds and upper bounds on the number of such grid lines are presented. The results in this paper extend and improve similar ones already described in the literature.