An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of three-dimensional grid-drawings is obtained as a corollary. Our results generalise to the setting of multi-dimensional polyline grid-drawings.

Additional Metadata
Journal Journal of Graph Algorithms and Applications
Citation
Bose, P, Czyzowicz, J. (Jurek), Morin, P, & Wood, D. (2004). The maximum number of edges in a three-dimensional grid-drawing. Journal of Graph Algorithms and Applications, 8(1), 21–26.