Abstract
We use basic results from graph theory to design two algorithms for constructing 3-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(√n× O(√n) × O(√n) box; each edge route contains at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second algorithm gives drawings having at most 3 bends per edge route. The drawings lie in an O(n)×O(n) × O(n) bounding box. Together, the two algorithms initiate the study of bend/bounding box trade-off issues for 3-dimensional grid drawings.
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